/.  2-°}r0-li, 


LIBRARY  OF  THE  THEOLOGICAL  SEMINARY 


PRINCETON,     N.    J. 


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ELEMENTS  OF  LOGICS 

3  192 


COMPRISING  X*^/C 


THE  DOCTKINE  OF  THE  LAWS  AND  PRODUCTS  OF 

THOUGHT,  AND  THE  DOCTRINE  OF  METHOD, 

TOGETHER  WITH  A  LOGICAL  PRAXIS. 


DESIGNED  EOR  CLASSES  AND  TOR.  PRIVATE  STUDY. 


HENRY  N.  DAT, 

AUTHOR  OF  "ART  OF  RHETORIC,"    "RHETORICAL  PRAXIS,"  ETC. 


Nam  neque  decipitur  ratio,  nee  decipit  unquam. 

The  mixture  of  those  things  by  speech,  which  by  nature  are  divided,  is  the  mother 
of  all  error. 


NEW  YORK: 
CHARLES  SCRIBNER  AND   COMPANY. 

1867. 


Entered  according  to  Act  of  Congress,  In  the  year  1867,  by 

Henry  N.  Day, 

in  the  Clerk's  Office  of  the  District  Court  for  the  District  of  Connecticut. 


RIVERSIDE,    CAMBRIDGE: 

STEREOTYPED    AND    PRINTED    BT 

H.    0.    HOUGHTON   AND    COMPANY. 


PREFACE 


The  present  work  is  designed  for  learners.  As  a  branch 
of  science,  the  study  of  Logic  commends  itself  by  very 
special,  not  to  say  preeminent  claims  to  all  lovers  of  learn- 
ing and  liberal  culture.  But  a  leading  motive  in  the  prepa- 
ration of  this  volume  has  been  to  furnish  a  needed  help  to  the 
training  of  thought  for  effective  communication  in  discourse. 
The  first  requisite  for  good  speaking  and  good  writing  is 
the  power  to  think  well ;  and  to  a  good  thinker,  the  study 
of  Logic  as  the  science  of  Thought  beat's  the  same  rela- 
tion as  the  study  of  mathematics  to  a  good  civil  engineer. 

The  plan  of  the  work  has  been  determined  by  this 
governing  design.  The  aim  has  been  to  develop  the  science 
in  strict  method.  From  the  determination  of  the  single 
radical  principle  of  Thought,  its  Laws  and  the  forms  of 
its  Products  have  been  methodically  evolved  ;  and  the  Doc- 
trine of  Method  with  the  Exercises  is  but  the  end  and 
result  toward  which  the  unfolding  of  the  Doctrine  of  the 
Elements  of  Thought  has  steadily  tended.  The  barbarous 
terminology  of  the  Scholastic  Logic,  shown  by  Sir  Wil- 
liam Hamilton  to  be  as  erroneous  as  useless,  is  discarded, 
except  so  far  as  seemed  necessary  for  understanding  the 
forms  in  which  it  has  entered  and  modified  general  liter- 
ature. The  Exercises  are  prepared  for  the  help  of  the 
teacher,  rather  than  to  be  used  just  as  they  are  presented, 


iv  PREFACE. 

except,  perhaps,  in  small  classes,  where  free  conversational 
discussion  and  criticism  are  practicable,  and  in  private 
study.  For  large  classes  there  may  be  found  necessary 
special  adaptations  of  the  material  here  furnished,  which 
may  be  used  to  suggest  other  exercises  or  to  furnish  op- 
portunity of  ready  selection. 

The  hope  that  this  object  of  training  for  effective  think- 
ing, and  especially  with  reference  to  the  construction  of 
Discourse,  may  be  better  accomplished  than  through  other 
published  treatises  on  Logic,  has  been  one  principal  induce- 
ment to  prepare  the  present  work.  But  some  new  things 
will  be  found  to  characterize  it,  which,  if  approved  and 
accepted  as  valuable  contributions  to  the  advancement  of 
the  science,  may,  of  themselves,  justify  this  address  to  the 
public. 

These  contributions  are  in  part  to  be  found  in  the  fol- 
lowing particulars,  to  which  the  attention  of  the  cultivators 
of  the  science  is  particularly  solicited. 

1.  The  risnd  reduction  of  Thought  to  its  one  essential 
principle  —  that  of  Identity. 

2.  The  unfolding  of  the  Laws  and  of  the  forms  of  the 
Products  of  Thought  under  this  principle,  and  the  validat- 
ing of  each  of  them  by  it. 

3.  The  formal  derivation  of  the  Concept  and  of  the 
Reasoning  from  the  primitive  product  of  Thought  —  the 
Judgment  —  under  the  principle  regulative  of  all  Thought 
—  that  of  Identity. 

4.  The  determination  of  the  reciprocal  relations  and  dis- 
tinguishing characteristics  of  Concepts  in  respect  of  their 
peculiar  Quantities,  and  of  the  relations  of  Concepts  to  Lan- 
guage. 


PREFACE.  V 

5.  The  more  exact  discrimination  of  the  Thought-process 
itself  from  its  object-matter  or  datum. 

6.  The  determination  of  the  different  kinds  of  Wholes 
in  which  Thought  may  proceed,  and  the  discrimination  of 
those  founded  in  the  matter  or  datum  to  Thought  from 
those  which  are  the  pure  product  of  Thought  itself. 

7.  The  full  development  of  the  relationship  of  Part  to 
Complementary  Part  as  one  of  the  two  relationships  in 
which  all  Thought  proceeds,  equally  primitive  and  neces- 
sary with  that  of  Whole  to  Part ;  this  last  being  the  only 
one  recognized  hitherto  by  logicians,  who  have,  by  unavoid- 
able consequence,  been  obliged  to  give  a  one-sided  and 
therefore  essentially  imperfect  and  unsatisfactory  develop- 
ment of  the  whole  science,  and  either  to  exclude  the  con- 
sideration of  Inductive  Reasoning  altogether  or  to  give  an 
entirely  erroneous  and  pernicious  presentation  of  it. 

8.  The  formal  grounding  of  all  Induction,  so  far  as  a 
process  of  Thought,  on  this  relationship  of  Part  to  Comple- 
mentary Part,  with  a  full  unfolding  of  its  laws,  its  forms, 
and  its  uses. 

9.  The  more  exact  exposition  of  Logical  Disjunction,  of 
the  grounds  of  distinction  between  Contradictory  and  Con- 
trary Oppositions,  of  Modality  and  its  distinctions,  and  of 
Necessary  and  Contingent  Truth. 

10.  A  new  classification  of  Reasonings,  —  the  logical  con- 
sequence of  modifications  of  logical  doctrine  already  indi- 
cated. 

11.  A  new  system  of  Logical  Methodology,  more  pre- 
cisely defined  as  the  Doctrine  of  the  Conditions  of  Thought 
in  order  to  perfect  science. 

12.  A  Logical  Praxis,  comprising  copious  exercises  sep- 


Ti  PIIEFACE. 


arately  arranged  for  each  of  the  forms  of  the  various  prod- 


ucts of  Thought. 


A  free  use  has  been  made  of  the  elaborations  of  Sir 
William  Hamilton,  who,  however  defective  and  imperfect 
his  system  appears  in  his  posthumous  lectures,  has  done 
more  for  the  science,  it  may  perhaps  be  said  without  ex- 
travagance, than  all  that  has  been  done  for  it  since  the 
times  of  Aristotle.  In  some  cases,  where  his  language 
has  been  used,  it  has  been  modified  and  changecTto  make 
his  teachings  correspond  to  those  that  are  peculiar  to  the 
present  work.  These  borrowings  are  indicated  by  the  usual 
quotation  marks  without  more  special  reference,  and  with- 
out any  discrimination  of  Hamilton's  free  borrowings  from 
German  writers,  or  of  the  changes  made  in  his  statements. 
The  intended  uses  of  the  book  as  a  text-book  seemed  to 
forbid  the  incumbering  of  the  text  with  such  special  refer- 
ences, while  this  general  acknowledgment  will  enable  any 
critical  reader  to  ascertain  the  extent  to  which  these  bor- 
rowings have  been  carried. 


New  Haven,  Conn.,  November,  1866. 


CONTENTS. 


INTRODUCTION. 

PAGB 

§  1.  Definition  of  Logic 1 

§2.  Its  Utility  :  —  a.  Objective;  b.  Subjective    .        .        3-12 
§  3-6.  Its  Divisions 12-16 


PART  I. 

THE  ELEMENTS  OF   THOUGHT. 


CHAPTER  I. 

THE  NATURE   OF   THOUGHT. 


§  7.  Elements  of  Thought :  —  1.  Laws;  2.  Products     .  17 

§  8.  Thought  a  relative  Cognition 1 7-1 9 

§9.  Nomenclature  of  Attributes     ...         .         .        .       19,20 


CHAPTER  H. 

THE  LAWS   OP    THOUGHT. 

§  10-14.  The  Four  Laws  of  Thought :  —  1.  Of  Identity  ; 
2.  Of  Contradiction  ;  3.  Of  Disjunction;  4.  Of 
Exclusion 21-25 

§  15.  Quantity  in  all  Thought 25,  26 

CHAPTER  III. 

THE   WHOLES   IX   THOUGHT.      LOGICAL   POSTULATE. 

§  16,  17.  Kinds  of  Wholes 27-29 

§  18.  Hamilton's  Postulate 29,  30 


Vlll 


CONTENTS. 


CHAPTEK  IV. 

THE  PRODUCTS   OF  THOUGHT. — I.  JUDGMENTS. 

PAGE 

§  19,  20.  Judgment  defined  and  explained     .        .        .      81-35 
§  21,  22.  Terms  : — Subject ;  Predicate  .        .        .       35-38 

§  23.  The  Copula 38,  39 

§  24.  Division  of  Judgments 39-47 

§  25,  26.  —  1.  As  to  Quality:  —  Affirmative;  Negative; 

Disjunctive 48-51 

§  27.  —  2.  As  to  Modality:  —  Assertory;   Problematic; 

Apodictic 51,  52 

§  28.  —  3.  As  to  Degree  of  Identity  :  —  Identical ;  Par- 
tial ;  Tautological 52,  53 

§29,30.-4.  As   to  Character  of  Terms :— Categor- 
ical ;  Hypothetical ;  Hypothetico-Disjunct- 

ive 53-56 

§  31.  —  5.  As  to  Logical  Quantity :  —  Extensive  ;  Inten- 
sive   56, 57 

§  32.  —  6.  As  to  Kind  of  Whole :  —  Integrate ;  Substan- 
tial; Causal 57,58 

§  33.  Judgments  in  relation  to  one  another    .        .        .      58-61 


62-65 

65-72 

72-78 

78-86 
86-90 


CHAPTER  V. 

THE   PRODUCTS   OF   THOUGHT. — II.   CONCEPTS. 

§  34-38.   Formation  and  Essential  Nature  of  Concepts 
§  39.    Relations  to  Objects  and  to  Language  . 
§  40-44.    Quantity  of  Concepts :  —  Extensive   and  In- 
tensive       

§  45-50.   Relations  of  Concepts  in  Extension 

§  51-54.    Relations  of  Concepts  in  Comprehension 

CHAPTER  VI. 

THE  PRODUCTS  OF  THOUGHT.  —  III.  REASONINGS. 

§  55-58.  Nature,  Denominations,  and  Divisions  of  Rea- 
sonings     .......       91-94 

§  59-65.  Immediate  Reasonings  :  —  Conversion  ;  Quan- 
titative Restriction  ;  Modal  Restriction  ; 
Transference;    Disjunction ;    Composition     94-102 


CONTENTS.  ix 

PAGE 

§66-70.  Categorical  Syllogisms:  —  Deductive;  Induc- 
tive    102-118 

§  71-77.  Conditional  Syllogisms  :  —  Ponent  and  Tol- 
lent ;  Hypothetical ;  Dilemma  ;  Disjunct- 
ive     118-128 

§78-80.   Polysyllogism :  —  Epichirema ;  Sorites     .         .  128-131 

PART  II. 

METHODOLOGY. 

CHAPTER  I. 

METHOD   IN   GENERAL. 

§81.   Nature  of  Method 132,133 

§  82-87.   Threefold  Perfection  of  Science  :  —  Material ; 

Formal;  Verbal 133-146 

CHAPTER  II. 

METHOD   IN   SPECIAL.  —  METHODOLOGY  OF   JUDGMENTS. 

§  88.  The  Three  Conditions  of  Perfection  in  Judgments  147-149 
§89-95.    Special  Rules  of  Judgments         .         .         .       149-156 

CHAPTER  ILL 

METHODOLOGY   OF    CONCEPTS. 

§96.   The  Three  Conditions  of  Perfection  in  Concepts  .  157 

§97.  Objective  Law  of  Concepts  .  ....  157-163 
§98-108.     Subjective    Law:  — Logical     Definition; 

Analysis 163-180 

§  109.   Verbal  Law 180-182 

CHAPTER  IV. 

METHODOLOGY   OF   REASONINGS. 

§110.  Probation  and  Investigation  ....  183,184 
§111.  Objective  Law  of  Reasonings  ....  184,185 
§112-124.    Subjective  Law 185-206 


X  CONTENTS. 

PART  III. 

LOGICAL  PRAXIS. 

PAQH 

I.  Exercises  in  Judgments 207-214 

II.   Exercises  in  Concepts 214. 

III.  Exercises  in  Reasonings 214-222 

Appendix  A.   Induction 223-227 

"        B.   Origin  of  Language  ....  227-231 


INTRODUCTION. 


DEFINITION    OF    LOGIC. 

§  1.  Logic    is  the   Science  of  the   Laws   of   L   ic  de_ 
Thought  as  Thought.  fined- 

The  name,  Logic,  is  derived  from  Aoyos,  which  word  in 
Greek  had  a  twofold  meaning,  denoting  both  thought  0rigin  of 
and  the  expression  of  thought.  To  avoid  the  Name- 
ambiguity  thus  arising,  Aristotle  limits  the  term,  when  ap- 
plied to  thought,  by  the  definitive  rbv  eo-co  —  that  within  the 
mind  ;  and  when  applied  to  the  expression  of  thought,  —  to 
speech,  by  the  definitive  tov  e^co  —  that  without. 

It  has  been  a  point  much  discussed  whether  Logic  is  a 
science,  or  an  art,  or  neither,  or  both.  "  Plato  and  L  ic  a  gci. 
the  Platonists  received  it  as  a  science  ;  but  with  ence- 
them  Dialectic  was  coextensive  with  the  Logic  and  Metaphys- 
ics of  the  Peripatetics  taken  together.  By  Aristotle  himself, 
Logic  is  not  defined.  The  Greek  Aristotelians,  and  many 
philosophers  since  the  revival  of  letters,  deny  it  to  be  either 
science  or  art.  The  Stoics,  in  general,  viewed  it  as  a  science  ; 
and  the  same  was  done  by  the  Arabian  and  Latin  schoolmen. 
In  more  modern  times,  however,  many  Aristotelians,  all  the 
Ramists,  and  a  majority  of  the  Cartesians,  maintained  it  to 
be  an  art ;  but  a  considerable  party  were  found  who  defined 
it  as  both  art  and  science.  In  Germany,  since  the  time  of 
Leibnitz,  Logic  has  been  almost  universally  regarded  as  a 
science." 

By  a  science,  is  meant  only  a  branch  of  knowledge,  un- 
1 


2  INTRODUCTION. 

folded  in  systematic  method.  It  would  seem  superfluous  to 
attempt  a  formal  vindication  of  the  claims  of  Logic  tc  be 
thus  regarded. 

The  object-matter  of  Logic  is  Thought,  strictly  so  called, 
its  object-  as  ^e  product  of  the  Discursive  Faculty,  other- 
Matter.  wjse  capeci  the  Faculty  of  Comparison,  the  Under- 
standing, and  by  Hamilton,  the  Elaborative  Faculty.  This 
term,  thought,  has  been  used  to  include  any  act  of  conscious- 
ness, whether  a  cognition,  a  feeling,  or  a  volition.  It  has 
been  more  commonly  used  to  include  any  act  of  the  Intelli- 
gence —  any  cognitive  act.  But  as  the  object-matter  of 
Logic,  it  is  used  in  a  still  more  restricted  meaning  to  denote 
only  an  act  of  the  Discursive  Faculty  —  the  Faculty  of 
mediate  cognition.  Logic,  accordingly,  takes  no  account  of 
the  faculties  of  original  cognition  —  the  Presentative  Facul- 
ties of  Perception,  Self-Consciousness,  and  Intuition  ;  nor  of 
the  Faculties  of  Representative  Knowledge  —  Memory  and 
Imagination.  The  range  of  Thought  proper,  then,  is  far 
more  limited  than  the  bounds  of  the  Intelligence,  as  a  de- 
pai'tment  of  mental  activity  coordinate  with  the  feelings  and 
the  will.  And  of  the  several  Faculties  of  the  Intelligence, 
it  is  restricted  to  the  operations  of  but  one  —  the  Discursive 
Faculty,  or  Faculty  of  Comparison. 

The  distinctive  nature  of  Thought  may  be  indicated  in  a 
general  way  thus :  The  Faculties  of  original  cognition  first, 
as  a  condition  to  the  exercise  of  Thought,  present  to  the 
mind  one  or  another  of  their  several  ohjects.  These  objects, 
as  apprehended,  become,  as  cognitions,  the  materials  upon 
which  the  Faculty  of  Thought  then  commences  its  opera- 
tions. If,  for  example,  the  Faculty  of  Perception  present 
any  object,  as  a  Tree,  the  object  is  first  apprehended 
vaguely  and  simply  by  itself.  But  as  the  attention  is  con- 
centrated upon  it,  it  is  apprehended  as  standing  in  certain 
relations  —  either  in  external  relations  toother  objects  which 
with  it  make  up  a  certain  sphere  of  knowledge  to  us,  or  in 
internal  relations  to  some  of  its  own  parts  or  properties. 


INTRODUCTION.  3 

The  object,  thus  viewed,  in  relation  to  the  object  without  or 
to  the  part  or  property  within,  is  said  to  be  thought.  Before, 
the  tree  was  simply  perceived  —  known  simply  in  itself;  now 
it  is  known  relatively  to  something  else  —  to  some  object  ex- 
ternal to  itself,  or  to  some  internal  part  of  itself:  for  instance, 
externally,  as  distant  from  some  other  external  object ;  or, 
internally,  as  broadly-branched,  as  covered  with  foliage,  as 
fruit-bearing,  or  as  having  some  other  property  or  character. 
Thought,  then,  is  a  cognition,  not  immediate  and  irrelative, 
as  is  a  perception,  an  intuition,  an  imagination,  but  mediate 
and  relative  —  a  cognition  of  an  object  as  related  to  some- 
thing else.  We  think  the  tree,  when  we  apprehend  it  as  dis- 
tant, as  branching,  and  the  like  —  as  having  some  attribute. 

Logic,  thus,  as  the  science  of  Thought,  is  limited  to  a  single 
department  of  our  cognitive  functions  —  to  the  function  of 
relative  cognitions.  Its  more  precise  nature  will  be  exhibited 
in  the  sequel. 

§  2.  The   utility  of  Logical    Science   may  be  estimated 
from  the  inherent  excellence  and  interest  of  the   utility  of 
Science  itself,  and  from  its  value  as  a  Mental  Dis-   L°S1C' 
cipline  and  Instrument  of  Knowledge. 

Objectively,  as  a  science  to  be  acquired  and  understood, 
Logic  claims  a  twofold  consideration.  First,  in  (a)  object- 
respect  of  its  object-matter,  Human  Thought,  scie^of^3 
no  science  presents  more  commanding  induce-  Thought- 
ments  to  its  investigation  and  study.  The  mechanism  of 
Thought,  its  parts,  its  springs,  its  movements,  its  products,  its 
guides  and  principles,  —  no  subject  certainly  possesses  a  prior 
claim  to  the  consideration  of  Thought  itself  than  this  its  own 
mechanism.  All  science,  all  our  systematic,  methodical  know- 
ing, is  the  product  of  Thought.  Thought  introduces  into  the 
Temple  of  Truth.  The  first  truth  we  gain  is  given  us  by 
Thought,  and  all  subsequent  truth  is  equally  her  gift.  Per- 
ception and  Self-Consciousness  give  us  objects  of  knowledge, 
furnish  the  rude  materials  of  Thought.  But  their  products 
are,  in  themselves,  but  the  most  meagre,  vaguest  cognitions. 


4  INTRODUCTION. 

They  are  only  impressions.  It  is  the  prerogative  of  Thought 
to  attribute  to  these  vague  impressions  reality,  to  determine 
their  relations  to  the  universe  of  truth  around,  to  mark  the 
inner  properties  which  characterize  and  qualify  them. 

It  is  under  the  prompting  and  guidance  of  Thought,  indeed, 
that  Perception  itself  moves  on  from  the  most  indeterminate 
observations  to  full  and  definite  cognitions.  Without  the  aid 
of  Thought,  it  stumbles  and  falls  at  the  very  threshold  of 
knowledge.  The  keenest  eye  and  the  most  laborious  delving 
in  the  earth  can  at  best  uncover  but  little  of  the  story  of  the 
antediluvian  world.  Out  of  a  single  fragment  of  a  fossil, 
geological  Thought  reads  a  voluminous  history  of  life,  habits, 
conditions,  laws,  belonging  to  ages  before  the  flood.  The 
mere  observer  might  sweep  his  eye  over  volumes  of  an  an- 
cient language,  and  be  little  wiser  as  to  its  history  and  con- 
nections, its  laws  and  structure  ;  while  a  single  page  fur- 
nishes all  the  conditions  necessary  to  enable  the  disciplined 
Thought  of  the  philologist  to  determine  all.  The  great  part 
of  astronomical  facts,  of  such  as  are  attainable  without 
Thought,  were  known  to  the  early  Oriental  shepherds. 
Thought,  out  of  those  few  observations,  has  constructed  that 
magnificent  structure  of  modern  astronomy.  Indeed,  human 
Intelligence  would  be  little  elevated  and  expanded  above  and 
beyond  that  of  the  brute  without  the  Faculty  of  Thought. 
By  the  comparative  excellence  of  the  object-matter  of  Log- 
ical Science  may  we,  thus,  estimate  its  own  importance  and 
value. 

But  Logic  presents  another  peculiar  attraction,  as  a  Pure 
2.  As  Pure  Science.  Its  matter  lies  in  the  mind  itself;  and 
Science.  jj.  treats  0I1]y  0f  tlisxt  which  is  necessary  in  that 

matter.  It  has  this  feature  in  common  with  Mathematical 
Science.  They  both  found  themselves  upon  the  operations 
of  -the  same  faculty  —  the  Discursive  Faculty,  which,  if 
viewed  in  its  essential  characteristics,  and  exclusively  of  its 
conditions  and  accessories,  is  simply  an  identifying  faculty, 
ever  and  only  recognizing  the  same  and  the  different.     In 


INTRODUCTION.  5 

Mathematical  Science,  its  identities  are  those  which  are 
found  only  in  the  forms  in  which  Being  enters  into  our  ex- 
perience —  the  forms  of  Space  and  Time,  and  are  only  those 
of  the  equal,  the  more  and  the  less,  in  magnitude  and  number. 
In  Logical  Science,  the  identities  in  Being  itself,  as  it  comes 
into  our  experience,  —  the  same  and  the  different  there,  are 
in  addition  brought  into  view.  Now,  as  only  what  trans- 
pires within  its  own  realm  can  be  accepted  by  Thought  as 
strictly  necessary,  as  what  is  given  to  thought  must  be  ever 
taken  only  as  given,  —  must  be  assumed,  and  so  viewed  as 
only  problematical  —  all  necessary  matter  lies  in  thought ;  and 
as  Logic,  like  Mathematics,  takes  into  view  only  the  neces- 
sary in  thought  itself,  it  is,  as  conversant  only  with  the 
necessary,  a  Pure  Science.  Mathematics  and  Logic  are, 
thus,  as  the  only  sciences  of  pure  thought,  the  only  .sciences 
of  necessary  truth.  No  other  science  possesses  properly  the 
character  of  necessary  matter,  except  so  far  as  pure  thought 
enters  into  and  characterizes  it ;  and  wherever,  in  whatever 
department  of  knowledge,  pure  thought  enters,  there  is  ne- 
cessary truth.  There  is  here  discovered  an  eminent  inci- 
dental utility  of  Logical  Science  that  it  enables  us  to  discrim- 
inate readily  what  is  necessary  from  wdiat  is  at  best  but 
contingent  in  any  department  of  knowledge,  while  it  claims 
to  itself  all  those  distinctive  attractions  and  excellencies 
which  properly  belong  to  Pure  Science. 

Subjectively,  however,  as  Instrument  of  Knowledge  and 
of  Mental  Discipline,  Logic  claims  the  highest  con-   0>)  Subject- 

.,  .  ri        •  ive  Utility 

sideration  as  a  useful  science.  of  Logic. 

It  is,  indeed,  in  a  certain  restricted  sense,  only  a  Formal 
Instrument  of  Knowledge.  It  can  of  itself  effect  no  new  dis- 
covery  in  the  field  of  matter  from  which  it  derives  the  con- 
ditions of  its  operations.  We  cannot  begin  with  our  thought, 
and  out  of  that  evolve  being  —  construct  sciences  of  the  world 
external  to  thought.  It  is  but  gross  self-imposture  to  assume 
a  mere  form  of  thought,  an  empty  formula,  and  then,  out  of 
this,  educe  outward,  objective  reality.     It  is  no  function  of 


6  INTRODUCTION. 

Thought,  of  itself  to  amplify  any  science  in  respect  to  the 
proper  object-matter  of  that  science.  So  far  as  it  attempts 
this,  it  invades  the  territory  of  the  Presentative  Faculties, 
and  its  attempts  are  suicidal. 

Still,  Logic  is  true  Instrument  of  Knowledge.     It  prompts 

1.  As  Aid  to  and  guides  the  proper  Presentative  Faculties. 
Discovery.  Except  as  these  lead  on  to  Thought,  and  except 
as  Thought  elaborates  their  rude  and  indeterminate  cogni- 
tions, they  themselves  seem  to  lose  spring  and  motive  to 
exertion.  They  are,  to  a  great  extent  at  least,  blind,  also, 
and  need  to  be  directed  as  to  the  proper  objects  which  they 
are  to  apprehend  and  to  present  to  Thought.  How  much  of 
modern  astronomical  discovery  has  been  prompted  and  guided 
by  Thought  ?  Certain  relations  in  the  solar  system,  obtained 
by  pure,  scientific  Thought,  indicated  the  existence  of  plan- 
etary worlds  here  or  there  in  space  ;  and  the  telescope,  guided 
by  these  indications  of  Thought,  brought  the  unknown  worlds 
into  view.  Indeed,  a  large  proportion  of  the  new  discoveries 
that  are  made  in  the  progress  of  every  science  have  origi- 
nated in  what  have  been  vaguely  called  analogies,  which  have 
been  furnished  by  Thought.  And  it  is  the  province  of  Logic 
to  unfold  the  laws  that  govern  these  analogies,  determine 
their  conditions,  test  their  soundness  and  validity. 

Further,  all  proper  science  is  the  product  of  Thought,  and 

2.  As  Builder  lies  wholly  within  the  domain  of  the  Discursive 
of  Science.  Faculty  of  the  human  Intelligence.  The  cogni- 
tions of  Perception,  as  already  remarked,  are  vague  and  in- 
definite ;  the  cognitions  of  the  pure  Reason,  or,  as  it  has  been 
called,  the  Regulative  Faculty,  are  equally  without  limita- 
tion and  without  relation.  Science  is  relative  and  defined 
cognition.  It  is  the  proper  province  of  Logic  to  acquaint  u9 
with  the  laws  of  all  science,  or  all  relative  cognition,  and  thus, 
in  the  intelligent  application  of  these  laws,  to  conduct  us  to 
assured  knowledge. 

While  Thought  deals  only  with  cognitions,  with  what  is 
already  in  the  mind,  and  thus,  strictly  speaking,  originates 


INTRODUCTION".  7 

no  material  knowledge,  we  must  not  take  in  too  narrow  an 
application  the  truth  that  it  is  but  the  Formal  Instrument 
of  Knowledge.  Mathematics,  like  Logic,  is  a  Formal  Sci- 
ence, yet  our  knowledge  of  the  heavenly  bodies  has  been 
chiefly  furnished  to  us  by  Mathematics.  The.  facts  given  in 
observation  are  comparatively  meagre.  Astronomy  has  in 
fact  made  most  of  its  growth  since  the  time  of  Kepler  and 
Newton,  and  that  growth  has  been  effected  chiefly  by  math- 
ematicians, not  by  observers.  What  Mathematics  is  to  the 
outer  world,  Logic  is  to  the  inner  world  of  truth.  Neither 
can  do  anything  for  any  object  of  science,  till  the  object  is 
given  to  it ;  neither  can  start  forth  and  from  its  own  unde- 
rived  and  unacquired  resources  construct  any  system  of 
knowledge.  But  matter  being  given  it  in  very  meagre 
amounts,  and  each,  in  its  sphere,  can  build  up  vast  struct- 
ures of  true  knowledge ;  for  the  essential  qualities  of  any 
object  of  knowledge  are  very  few  in  comparison  with  the 
relative.  While  the  observed  attributes  increase  arithmet- 
ically, the  relations  of  thought  increase  with  the  rate  of  per- 
mutation and  combination.  When  a  fragment  of  a  bone  was 
presented  to  Cuvier,  he  was  enabled  in  thought  to  read  in  it 
the  size,  age,  habits,  the  specific  characteristics  of  the  animal 
to  which  it  belonged.  So  Thought,  out  of  a  fragment  of 
fact,  interprets  rich  and  vast  treasures  of  truth  through  its 
relations,  internal  and  external.  It  is  true  that  Losric  is  not 
Thought ;  it  is  true,  also,  that  men  think  without  Logic.  So 
Mathematics  is  not  Astronomy  ;  and  men  can  compute  without 
arithmetical  rules.  But  how  extremely  limited  is  all  such 
computation,  all  such  thought ;  and  at  best  how  uncertain  are 
its  results,  and  even  although  correct,  how  little  assurance 
do  these  results  give  to  the  ignorant  calculator  and  thinker  ? 
The  absolute  impotence  of  Logic,  of  Thought,  to  construct 
a  science  in  any  department,  without  the  matter  of  that  sci- 
ence being  previously  given  in  experience,  is  now  every 
where  recognized.  Not  so  distinctly  recognized  is  its  de- 
pendence on  the  other  faculty  or  source  of  knowledge  —  the 


8  INTRODUCTION. 

Regulative  Faculty  —  the  Reason  —  Common  Sense.  But 
if  not  its  absolute  impotence,  still  its  impotence  to  any  thing 
valuable  or  worthy,  is  just  as  real  without  the  ideas  of  the 
Reason,  as  without  the  facts  of  experience.  Of  what  worth 
would  science  be  to  us,  even  were  it  possible,  that  proceeded 
independently  of  our  ideas  of  Space  and  Time  ;  of  Being, 
Substance,  Cause ;  of  Truth,  Beauty,  Rectitude,  and  Good- 
ness? Logic  can  venture  forth  not  one  step  in  safety,  or  in 
promise  of  attaining  any  worthy  result,  except  as  these  great 
ideas  of  the  Reason  guide  and  animate,  as  its  processes  are 
upon  and  through  these  fundamental  data  of  the  Intelligence. 
But  in  turn,  these  grand  ideas  are  of  little  worth  to  us,  ex- 
cept as  Thought  apprehends  them,  scans  them  in  their  mani- 
fold relations,  and  then  determines  and  indicates  these  rela- 
tions. 

Logic,  indeed,  is  not  Thought ;  it  is  only  Thought  applied 
to  Thought;  the  science  of  Thought,  or  still  more  precisely, 
the  science  of  the  necessary  in  Thought.  But  this  very  lim- 
itation of  Logic  suggests  its  immeasurable  utility  to  the  spirit 
of  man,  whose  dignity  consists  so  much  in  Thought.  If 
Logic  is  not  Thought,  it  )-et  presides  over  Thought,  and  pre- 
scribes its  function  and  its  sphere.  It  preserves  us,  thus, 
from  illusions  and  phantoms,  which  are  for  the  most  part 
occasioned  by  the  confounding  of  experiences  and  thoughts ; 
and  the  consequent  imposition  of  thoughts  for  objects. 

Logic,  moreover,  opens  the  way  for  Thought,  and  by  pre- 
senting occasions,  calls  it  forth  into  exercise.  It  teaches 
how  it  may  fasten  upon  an  object  of  experience,  or  an  idea 
of  the  Reason  ;  trace  out  its  relations  ;  determine  its  proper- 
ties, its  conditions,  its  bearings.  The  chief  obstacle  to  think- 
ing is  ignorance  how  to  think.  Matter  enough  is  given  in 
every  outlook  upon  the  external  world,  in  every  glance 
turned  inward  upon  our  mental  experience,  to  provoke  and 
to  sustain  endless  thought.  Thought  does  not  go  forth  as 
this  gate  of  occasion  opens  to  it,  because  it  does  not  see. 
Logic  opens  its  eyes  upon  the  relations  in  their  diversity, 
through  which  it  may  go  forth  to  its  work. 


INTRODUCTION.  9 

Logic,  further,  completes  and  perfects  Thought.  Thought 
necessarily  remains  feeble  and  immature,  except  as  it  is 
developed  and  matured  by  Logic.  As  Mathematics  enables 
Thought  to  carry  its  computations  to  indefinite  limits,  and 
to  pace  off  the  measureless  skies,  while  the  savage  can  only 
compute  but  several  scores,  and  can  measure  only  where  the 
foot  can  tread  ;  so  Logic  not  only  carries  Thought  forward  in 
every  particular  direction  to  its  remotest  bounds,  but  also 
carries  it  over  the  entire  field  of  its  explorations,  so  that  no 
part  shall  be  overlooked. 

Logic  is  useful,  also,  in  correcting  our  knowledge.  It  has 
been  justly  termed  a  medicine  of  the  mind,  as  it  3.  as  Correc- 
helps  to  purge  it  from  errors  which  impair  and  tive  of  Error. 
vitiate  its  healthful  activity.  -It  does  not  directly  heal  the 
imperfection  or  error  that  may  have  crept  into  its  opera- 
tions at  the  original  presentation  of  its  matter.  But  when, 
by  its  sure  procedure,  it  discovers  that  the  original  datum 
as  presented  to  it  has  led  to  results  that  are  not  in  har- 
mony with  its  already  ascertained  truths,  or  that  involve 
contradictory  relations,  or  that  do  not  admit  of  being  per- 
fectly brought  under  the  complete  and  necessary  conditions 
of  thought,  by  detecting  the  fact  of  error  and  its  probable 
source,  it  guides  and  helps  to  the  needful  correction  by  the 
proper  presentative  faculty ;  precisely  as  Mathematics,  al- 
though like  Logic  a  purely  formal  science,  can  show  that 
there  is  error  somewhere  in  the  original  measurement,  or  the 
running  of  the  lines  of  a  survey,  if  the  bearings  and  distances 
as  given  will  not  admit  of  being  plotted  into  a  bounded  field, 
and  may  indicate  also,  possibly,  where  the  error  originated, 
so  that  it  may  be  corrected  by  new  survey. 

Logic,  still  further,  is  of  eminent  utility  in  furnishing  the 
proper  assurance  of  Truth.  If  it  is  much  to  know,  4  Ag  as_ 
it  is  often  more  to  know  that  we  know  ;  to  be  rea-  surins truth- 
sonably  assured  that  what  we  accept  as  true  is  indeed  true,  as 
verified  by  the  only  possible  criteria  of  truth  within  the  reach 
of  the  human  mind.     Confidence  in  the  correctness  of  the 


10  INTRODUCTION. 

procedures  of  Thought,  confidence  in  the  validity  of  the  re- 
sults of  Thought,  is  one  of  the  leading  conditions  of  success 
in  all  thinking.  To  be  in  doubt  whether  we  are  on  the  road 
to  truth,  whether  we  are  in  possession  of  the  requisite  means 
of  attaining  it,  whether  what  we  at  last  have  reached  is  the 
truth  we  seek,  is  very  mental  imbecility.  It  is  the  preroga- 
tive and  proper  function  of  Logic,  as  the  Science  of  the  Laws 
of  Thought,  to  remove  the  grounds  of  such  doubt,  to  indicate 
and  so  to  assure  as  certain  the  way  to  truth,  and  to  impart 
credibility  to  the  results  of  Thought.  It  is  true  that,  in  large 
departments  of  our  knowledge,  what  we  know  can  have  at 
best  but  the  character  of  probable  truth,  never  that  of  abso- 
lute certainty.  But  it  is  the  part  of  Logic  to  point  out  just 
where  the  lines  that  separate  probable  from  absolute  certainty 
run,  and  also  to  discover  just  where  the  contingency  in  im- 
perfect knowledge  attaches  ;  the  nature,  the  source,  the  ex- 
tent, the  means,  if  any,  of  removal  of  all  that  impairs  our 
knowledge.  Such  is  the  assurance  that  Logic  gives  to  our 
thinking. 

"  But  it  is  not  only  by  affording  knowledge  and  skill  that 
6.  As  in-  Logic  is  thus  useful ;  it  is  perhaps  equally  con- 
toe°Under-  ducive  to  the  same  end  by  bestowing  power.  The 
standing.  retortion  of  thought  upon  itself —  the  thinking  of 
thought  —  is  a  vigorous  effort,  and,  consequently,  an  invigor- 
ating exercise  of  the  Understanding  ;  and  as  the  Understand- 
ing  is  the  instrument  of  all  scientific,  of  all  philosophical  specu- 
lation, Logic,  by  preeminently  cultivating  the  understanding, 
in  this  respect  likewise  vindicates  its  ancient  title  to  be  viewed 
as  the  best  preparatory  discipline  for  Philosophy  and  the 
sciences  at  large. 

"  But  Logic  is  further  useful  as  affording  a  Nomenclature 
6.  As  af-  °f  tne  laws  by  which  legitimate  thinking  is  gov- 
fording  a  so i-   erned,  and  of  the  violations  of  these  laws,  through 

entinc     No-  o 

menciature.     which  thought  becomes  vicious  or  null. 

"  Words  do  not  give  thoughts  ;  but  without  words,  thoughts 
could  not  be  fixed,  limited,  and  expressed.     They  are,  there- 


INTRODUCTION.  11 

fore,  in  general,  the  essential  condition  of  all  thinking  worthy 
of  the  name.  Now,  what  is  true  of  human  thought  in  gen- 
eral, is  true  of  Logic  and  Rhetoric  in  particular.  The  no- 
menclature in  these  sciences  is  the  nomenclature  of  certain 
general  analyses  and  distinctions,  which  express  to  the  initi- 
ated, in  a  single  word,  what  the  uninitiated  could  (supposing, 
what  is  not  probable,  that  he  could  perform  the  relative  proc- 
esses) neither  understand  nor  express  without  a  tedious  and 
vague  periphrasis  ;  while,  in  his  hands,  it  would  assume  only 
the  appearance  of  a  particular  observation,  instead  of  a  par- 
ticular instance  of  a  general  and  acknowledged  I'ule.  To 
take  a  very  simple  example  :  there  is  in  Logic  a  certain 
sophism,  or  act  of  illegal  inference,  by  which  two  things  are, 
perhaps  in  a  very  concealed  and  circuitous  manner,  made  to 
prove  each  other.  Now,  the  man  unacquainted  with  Logic 
may  perhaps  detect  and  be  convinced  of  the  fallacy  ;  but  how 
will  he  expose  it  ?  He  must  enter  upon  a  long  statement  and 
explanation,  and  after  much  labor  to  himself  and  others  he 
probably  does  not  make  his  objection  clear  and  demonstrative 
after  all.  But  between  those  acquainted  with  Logic  the 
whole  matter  would  be  settled  in  two  words.  It  would  be 
enough  to  say  and  show  that  the  inference  in  question  in- 
volved a  circle,  and  the  refutation  is  at  once  understood  and 
admitted.  It  is  in  like  manner  that  one  lawyer  will  express 
"  to  another  the  ratio  decidendi  of  a  case  in  a  single  technical 
expression ;  while  their  clients  will  only  perplex  themselves 
and  others  in  their  attempts  to  set  forth  the  merits  of  their 
cause.  Now,  if  Logic  did  nothing  more  than  establish  a  cer- 
tain number  of  decided  and  decisive  rules  in  reasoning,  and 
afford  us  brief  and  precise  expressions  by  which  to  bring  par- 
ticular cases  under  these  general  rules,  it  would  confer  on 
all  who  in  any  way  employ  their  intellect  —  that  is,  on  the 
cultivators  of  every  human  science  —  the  most  important  ob- 
ligation. For  it  is  only  in  the  possession  of  such  established 
rules,  and  of  such  a  technical  nomenclature,  that  we  can  ac- 
complish, with  facility,  and  to  an  adequate  extent,  a  criticism 


12  INTRODUCTION'. 

of  any  work  of  reasoning.  Logical  language  is  thus,  to  the 
general  reasoner,  what  the  notation  of  Arithmetic,  and  still 
more  of  Algebra,  is  to  the  mathematician.  Both  enable  us 
to  comprehend  and  express,  in  a  few  significant  symbols,  what 
would  otherwise  overpower  by  their  complexity ;  and  thus  it 
is  that  nothing  would  contribute  more  to  facilitate  and  extend 
the  faculty  of  thinking,  than  a  general  acquaintance  with  the 
rule(s  and  language  of  Logic." 

§  3.  Logic  may  be  divided  on  different  principles  of  divis- 
Divisions  of  'on  m*°  different  sets  of  species,  of  which  the 
Logic.  more  important  are  the  three  following  : 

,    „.   .  First,  in  reference  to  the  mind  or  thinking  sub- 

1.    Object-         m  ....  .  .        .  , 

ivean^ub-  ject,  Logic  is  divided  into  Objective  (Logica  Sys- 
tematica) and  Subjective  (Logica  Habitualis). 

"  By  Objective  or  Systematic  Logic  is  meant  that  comple- 
ment of  doctrines  of  which  the  science  of  Logic  is  made  up ; 
by  Subjective  or  Habitual  Logic  is  meant  the  speculative 
knowledge  of  these  doctrines  which  any  individual,  as  Soc- 
rates, Plato,  Aristotle,  may  possess,  and  the  practical  dex- 
terity with  which  he  is  able  to  apply  them. 

u  Now,  it  is  evident  that  both  these  Logics,  or  rather,  Logic 
considered  in  this  twofold  relation,  ought  to  be  proposed  to 
himself  by  an  academical  instructor.  We  must,  therefore, 
neglect  neither.  Logic  considered  as  a  system  of  rules,  is 
only  valuable  as  a  mean  toward  Logic  considered  as  a  habit 
of  the  mind  ;  and,  therefore,  a  logical  instructor  ought  to  do 
what  in  him  lies  to  induce  his  pupils,  by  logical  exercise,  to 
digest  what  is  presented  to  them  as  an  objective  system  into 
a  subjective  habit.  Logic  in  both  these  relations  belongs  to 
us,  and  neither  can  be  neglected  without  compromising  the 
utility  of  the  study. 

§  4.  "  In  the  second  place,  by  relation  to  its  application  or 
2.  Abstract  non-application  to  objects,  Logic  is  divided  into 
and  concrete   Abstract  or  General,  and  into  Concrete  or  Spe- 

or  Special.        cial. 

"  Abstract  Logic  considers  the  laws  of  thought  as  potentially 


INTRODUCTION.  13 

applicable  to  the  objects  of  all  arts  and  sciences,  but  as  not 
actually  applied  to  those  of  any  ;  Concrete  Logic  considers 
these  laws  in  their  actual  and  immediate  application  to  the 
object-matter  of  this  or  that  particular  science.  The  former 
of  these  is  one,  and  alone  belongs  to  philosophy,  whereas  the 
latter  is  as  multiform  as  the  arts  and  sciences  to  which  it  is 
relative. 

"  This  division  of  Logic  does  not  remount  to  Aristotle,  but 
it  is  found  in  his  most  ancient  commentator,  Alexander  the 
Aphrodisian,  and,  after  him,  in  most  of  the  other  Greek 
Logicians.  Alexander  illustrates  the  opposition  of  the  logic 
divorced  from  things,  to  the  logic  applied  to  things,  by  a 
simile.  "  The  former,"  he  says,  "  may  be  resembled  to  a 
geometrical  figure,  say  a  triangle,  when  considered  abstractly 
and  in  itself;  whereas  the  latter  may  be  resembled  to  the 
same  triangle,  as  concretely  existing  in  this  or  that  partic- 
ular matter :  for  -a  triangle  considered  in  itself  is  ever  one 
and  the  same  ;  but  viewed  in  relation  to  its  matter,  it  varies 
according  to  the  variety  of  that  matter ;  for  it  is  different  as 
it  is  of  silver,  gold,  lead  —  as  it  is  of  wood,  of  stone,  etc. 
The  same  holds  good  of  Logic.  General  or  Abstract  Logic 
is  always  one  and  the  same  ;  but  as  applied  to  this  or  to  that 
object  of  consideration,  it  appears  multiform.'  So  far  Alex- 
ander. This  appearance  of  multiformity,  however,  is  not 
real ;  for  the  mind  has  truly  only  one  mode  of  thinking,  one 
mode  of  reasoning,  one  mode  of  conducting  itself  in  the 
investigation  of  truth,  whatever  may  be  the  object  on  which 
it  exercises  itself.  Logic  may,  therefore,  be  again  well  com- 
pared to  the  authority  of  a  universal  empire  —  of  an  em- 
pire governing  the  world  by  common  laws.  In  such  a 
dominion  there  are  many  provinces,  various  regions,  and 
different  prefectures.  There  is  one  prefect  in  Asia,  another 
in  Europe,  a  third  in  Africa,  and  each  is  decorated  by  differ- 
ent titles ;  but  each  governs  and  is  governed  by  the  common 
laws  of  the  empire  confided  to  his  administration.  The 
nature  of  General   Logic  may  likewise   be   illustrated  by 


14  INTRODUCTION. 

another  comparison.  The  Thames,  for  instance,  in  passing 
London,  is  a  single  river  —  is  one  water  —  but  is  there  ap- 
plied to  many  and  different  uses.  It  is  employed  for  drink- 
ing, for  cooking,  for  brewing,  for  washing,  for  irrigation,  for 
navigation,  etc.  In  like  manner,  Logic  in  itself  is  one :  as  a 
science  or  an  art,  it  is  single  ;  but  in  its  applications,  it  is  of 
various  and  multiform  use  in  the  various  branches  of  knowl- 
edge, conversant  be  it  with  necessary,  or  be  it  with  contin- 
gent matter.  Or  further,  to  take  the  example  of  a  cognate 
science,  if  any  one  were  to  lay  down  different  grammars  of  a 
tongue,  as  that  may  be  applied  to  the  different  purposes  of 
life,  he  would  be  justly  derided  by  all  grammarians,  indeed 
by  all  men  ;  for  who  is  there  so  ignorant  as  not  to  know  that 
there  is  but  one  grammar  of  the  same  language  in  all  its 
various  applications  ? 

"  Thus,  likewise,  there  is  only  one  method  of  reasoning, 
which  all  the  sciences  indifferently  employ  ;  and  although  men 
are  severally  occupied  in  different  pursuits,  and  although  one 
is,  therefore,  entitled  a  Theologian,  another  a  Jurist,  a  third  a 
Physician,  and  so  on,  each  employs  the  same  processes,  and 
is  governed  by  the  same  laws,  of  thought.  Logic  itself  is, 
therefore,  widely  different  from  the  use  —  the  application  of 
Logic.  For  Logic  is  astricted  to  no  determinate  matter,  but 
is  extended  to  all  that  is  the  object  of  reason  and  intelligence. 
The  use  of  Logic,  on  the  contrary,  although  potentially  ap- 
plicable to  every  matter,  is  always  actually  manifested  by 
special  reference  to  some  one.  In  point  of  fact,  Logic,  in  its 
pai'ticular  applications,  no  longer  remains  logic,  but  becomes 
part  and  parcel  of  the  art  or  science  in  which  it  is  applied. 
Thus  Logic,  applied  to  the  objects  of  geometry,  is  nothing 
else  than  Geometry  ;  Logic,  applied  to  the  objects  of  physics, 
nothing  else  than  Natural  Philosophy.  "We  have,  indeed, 
certain  treatises  of  Logic  in  reference  to  different  sciences, 
which  may  be  viewed  as  something  more  than  these  sciences 
themselves.  For  example :  we  have  treatises  on  Legal 
Logic,  etc. ;  but  such  treatises  are  only  introductions  —  only 


INTRODUCTION.  15 

methodologies  of  the  art  or  science  to  which  they  relate. 
For  such  special  logics  only  exhibit  the  mode  in  which  a 
determinate  matter  or  object  of  science,  the  knowledge  of 
which  is  presupposed,  must  be  treated,  the  conditions  which 
regulate  the  certainty  of  inferences  in  that  matter,  and  the 
methods  by  which  our  knowledge  of  it  may  he  constructed 
into  a  scientific  whole.  Special  Logic  is  thus  not  a  single 
discipline,  not  the  science  of  the  universal  laws  of  thought, 
but  a  congeries  of  disciplines,  as  numerous  as  there  are 
special  sciences  in  which  it  may  be  applied.  Abstract  or 
General  Logic,  on  the  contrary,  in  virtue  of  its  universal 
character,  can  only  and  alone  be  one ;  and  can  exclusively 
pretend  to  (he  dignity  of  an  independent  science.  This, 
therefore,  likewise  exclusively  concerns  us. 

§  5.  "  In  the  third  place,  considered  by  reference  to  the 
circumstances  under  which  it  can  come  into  exer-  3  Pure  and 
cise  by  us,  Logic  is  divided  into  Pure  and  Modi-  Modified- 
fied.  Pure  Logic  considers  the  laws  of  thought  proper,  as 
contained  a  'priori  in  the  natui-e  of  pure  intelligence  itself. 
Modified  Logic  exhibits  these  laws  as  modified  in  their  act- 
ual applications  by  certain  general  circumstances  external 
and  internal,  contingent  in  themselves,  but  by  which  hu- 
man thought  is  always  more  or  less  influenced  in  its  mani- 
festations. 

"  Pure  Logic  considers  Thought  Proper  simply  and  in  it- 
self, and  apart  from  the  various  circumstances  by 

zv.  .  Pure  Logic. 

which  it  may  be  affected  in  its  actual  application. 
Human  thought,  it  is  evident,  is  not  exerted  except  by  men 
and  individual  men.  By  men,  thought  is  not  exerted  out  of 
connection  with  the  other  constituents  of  their  intellectual 
and  moral  character,  and,  in  each  individual,  this  character 
is  variously  modified  by  various  contingent  conditions  of 
different  original  genius,  and  of  different  circumstances  con- 
tributing to  develop  different  faculties  and  habits.  Now, 
there  may  be  conceived  a  science  which  considers  Modified 
thought  not  merely  as  determined  by  its  necessary  Loglc- 


16  INTRODUCTION. 

and  universal  laws,  but  as  contingently  affected  by  the  empir- 
ical conditions  under  which  thought  is  actually  exerted  ; 
which  shows  what  these  conditions  are,  how  they  impede, 
and,  in  general,  modify,  the  act  of  thinking ;  and  how,  in 
fine,  their  influence  may  be  counteracted.  This  science  is 
Modified  or  Concrete  Logic.  It  is  identical  with  what  Kant 
and  other  philosophers  have  denominated  Applied  Logic. 

"  Modified  Logic,  however,  is  neither  an  essential  part  nor 
an  independent  species  of  General  Logic,  but  a  mere  mixt- 
ure of  Logic  and  Psychology,  and  may,  therefore,  be  called 
Logical  Psychology  or  Psychological  Logic.  There  is  thus 
in  truth  only  one  Logic,  that  is,. Pure  or  Abstract  Logic." 

§  6.  Pure  Logic  may  be  most  conveniently  distributed 
Parts  of  into  two  parts  ;  —  the  one  of  which  shall  expound 
Pure  Logic.  ^e  cont|itjons  0f  thinking  in  itself,  irrespectively 
of  the  proper  end  of  thinking ;  the  other  shall  set  forth  the 
conditions  of  thinking  in  order  to  the  attainment  of  truth  or 
science,  as  the  proper  end  of  all  thinking.  In  the  first  part, 
accordingly,  should  be  exhibited  the  elements  of  thought  in 
itself,  the  Absolute  Conditions  of  Thought ;  and  in  the  second 
part,  the  elements  of  thought  in  its  relations  to  Truth  or 
Science,  the  Relative  Conditions  of  Thought. 

Pure  Logic,  then,  will  embrace  the  two  parts  of — 

I.  The  Doctrine  of  the  Essential  Elements  of  Thought ; 
and, 

II.  The  Doctrine  of  Method  or  Methodology. 

To  these  two  Parts  of  Systematic  Logic  should  be  added 
another  of  Subjective  Logic,  in  the  form  of  a  Logical 
Praxis. 


PURE    LOGIC. 

PART   I. 

THE  ELEMENTS  OF  THOUGHT. 

— * — 

CHAPTER  I. 

THE   NATURE    OF   THOUGHT. 

§  7.  The  First  Part  of  Logical  Doctrine  embraces  the 
Doctrine  of  the  Elements  of  Thought.  These  Elements  con- 
sist of  the  necessary  Conditions  of  Thought,  and  the  Prod- 
ucts of  Thought.  This  first  part  of  Logic  accordingly  com- 
prehends two  leading  departments,  treating  severally  — 

I.  Of  the  Laws  of  Thought  ; 

II.  Of  the  Products  of  Thought. 

In  order,  however,  to  the  more  exact  determination  of  the 
nature  and  validity  of  these  Laws  of  Thought,  and  of  the 
characters  and  relationships  of  these  Products  of  Thought,  it 
will  be  necessary  to  define,  more  precisely  than  we  have  yet 
done,  the  nature  of  Thought  itself,  so  far  as  Logic  takes  cog- 
nizance of  it. 

§  8.  Thought,  in  its  limited  import,  as  denoting  the  pro- 
duct of  the  Discursive  Intelligence,  is  a  relative  Thought  a 

relative  cog- 
COgnitlOn.  nitiou. 

In  Perception,  the  cognition  is  immediate  and  independent ; 
the  knowledge  is  of  something  considered  directly  and  in 
itself.  When  I  see  an  individual  object  thus,  —  say  Buceph- 
alus, or  Highflyer,  —  or  when  I  represent  him  in  imagination, 
I  have  a  direct  and  immediate  apprehension  of  a  certain  object 
2 


18  PURE  LOGIC. 

in  and  through  itself.  There  is  no  relation  in  such  a  cogni- 
tion as  a  mere  perception.  But  such  is  the  nature  of  the  com- 
plex activity  of  the  human  mind,  and  such  the  connection 
between  its  several  energies,  that  while  the  activity  is  always 
first  awakened  by  a  perception,  every  perception  draws  on, 
as  by  a  necessity,  the  exertion  of  other  energies.  Thus,  when 
I  perceive  Bucephalus,  I  at  once  have  awakened  in  my  mind 
the  intuitive  idea  of  existence.  There  are  thus  present  in 
the  mind  at  the  same  time  the  two  cognitions  ;  that  of  Per- 
ception —  Bucephalus  —  and  that  of  Intuition  —  Existence. 
These  two  cognitions  are  accordingly  viewed  in  relation, 
each  to  the  other ;  and  the  recognition  of  this  relation  is 
clearly  distinguishable  from  the  two  prior  cognitions.  It  is 
a  new  cognition,  —  a  cognition  not  of  Bucephalus  by  himself, 
not  of  Existence  by  itself,  but  of  Bucephalus  as  existing. 
This  is  a  thought,  a  judgment ;  and  is  manifestly  a  relative 
cognition  or  knowledge  ;  a  cognition,  not  of  objects  by  or  in 
themselves,  but  of  objects  in  relation  to  each  other ;  a  cogni- 
tion, in  fact,  of  related  cognitions,  not  of  related  external 
objects. 

The  second  cognition  into  relation  with  which  the  cognition 
of  Bucephalus  is  thus  brought  through  the  restless  and  di- 
verse energy  of  the  mind,  is  not,  necessarily  and  always,  it 
should  be  noticed,  an  Intuitive  cognition.  It  may  be  another 
Perception ;  as,  for  instance,  on  perceiving  Bucephalus,  I 
may  also  perceive  a  part  or  a  property  belonging  to  him,  as 
that  he  is  four-footed  —  quadruped.  As  before,  the  cognition 
of  Existence,  so  now  that  of  quadruped  is  brought  into  rela- 
tion with  the  cognition  of  Bucephalus  ;  and  the  relative  cog- 
nition, the  thought  of  Bucephalus  as  quadruped  comes  up  in 
the  mind. 

It  is  obvious  that  thought,  as  thus  a  relative  cognition  — 
a  cognition  of  cognitions  related  to  each  other  —  necessarily 
respects  two  cognitions,  and  two  only  ;  inasmuch  as,  although 
either  one  may  be  itself  complex,  the  relation  can  properly 
subsist  between  two  only.     If,  in  the  combinations  of  thought 


THE  NATURE  OF  THOUGHT.  19 

and  in  abbreviations  of  verbal  expression,  more  than  two 
factors  seem  to  be  brought  into  relation,  they  can  always  be 
reduced  to  two.  Thought  is,  accordingly,  ever  and  essentially 
a  cognition  of  a  duality. 

In  the  instances  given,  the  second  cognition  in  each  case  is 
one  that  is  internal  in  relation  to  the  first ;  existence  and 
quadruped  being  qualities  recognized  as  belonging  to  Buceph- 
alus. In  these  cases,  Bucephalus  is  viewed  as  a  whole,  of 
which  existence  and  quadruped  are  severally  parts.  But  the 
second  cognition  may  be  external  to  the  first ;  Bucephalus 
being  viewed  as  a  part  in  relation  to  some  other  object,  as  to 
Alexander.  The  thought  then  arises,  Bucephalus  is  Alexan- 
der's. The  relation  recognized  in  thought  between  the  first 
and  second  cognitions,  which  are  its  objects,  may  thus  be 
either  internal  or  external  to  the  first.  But  the  judgment  in 
all  cases  is  a  relative  cognition  ;  and  the  judgment,  as  will  be 
shown  hereafter,  is  the  primitive  form  of  thought  from  which 
the  two  others,  the  concept  and  the  reasoning,  are  derived. 
All  thought  thus  is  a  relative  cognition. 

Still  further,  it  is  apparent  that,  when  I  think  any  thing,  I 
view  it  in  relation  to  one  only  of  many  other  possible  cogni- 
tions. I  may  think  Bucephalus  as  existing,  or  as  four-footed, 
or  as  Alexander's,  and  so  on  indefinitely.  There  are  so  many 
different  modes  of  thought.  As  I  cannot  think  any  thing 
without  thinking  it  in  some  particular  mode,  that  is,  in  re- 
lation to  some  attribute,  so  these  modes,  possible  to  thought, 
are  of  unlimited  diversity. 

Logicians  have  designated  these  modes  by  different  terms, 
which  it  will  be  of  convenience  to  present  and  explain  in 
connection. 

§  9.  "  When  we  think  a  thing,  this  is  done  by  conceiving  it 
as  possessed  of  certain  modes  of  being,  or  quali-   mt 

r  .  The  van- 

ties,  and  the  sum  of  these  qualities  constitutes  a   ous  terms  °y 

/  x  >     /  which  the 

concept  or  notion  (vorj/jLa,  (.vvoia,  lirivoia,  conceptum,   modes  of 
conceptus,  notio).      As  these  qualities  or  modes  istence  are 
(7rotoT^T€s,  qualitates,  modi)   are  only  identified     esigna  e 


20  PURE  LOGIC. 

with  the  thing  by  a  mental  attribution,  they  are  called  attri- 
butes (KaTrr/opov/xeva,  attributa)  ;  as  it  is  only  in  or  through 
them  that  we  say  or  enounce  aught  of  a  thing,  they  are 
called  predicates,  predicables,  and  predicaments,  or  categories, 
these  words  bein£  here  used  in  their  more  extensive  signifi- 
cation  ^KaTrryopiat,  Ka.Tr)yopy)p.a.ra,  Ka.T7iyopovp.tva,  prcedicata, 
pradicabilia,  pr&dicamenta )  ;  as  it  is  only  in  and  through 
them  that  we  recognize  a  thing  for  what  it  is,  they  are  called 
notes,  signs,  marks,  characters  (nota,  signa,  characteres,  dis- 
crimina)  ;  finally,  as  it  is  only  in  and  through  them  that  we 
become  aware  that  a  thing  is  possessed  of  a  peculiar  and 
determinate  existence,  they  are  called  properties,  differences, 
determinations  (proprietates,  determinationes).  As  conse- 
quent on,  or  resulting  from,  the  existence  of  a  thing,  they 
have  likewise  obtained  the  name  of  consequents  (l-nop-tva, 
consequentia,  etc).  What  in  reality  has  no  qualities,  has  no 
existence  in  thought  —  it  is  a  logical  nonentity  ;  hence,  e  con- 
verso,  the  scholastic  aphorism  —  non-entis  nulla  sunt  pradi- 
cata.  What,  again,  has  no  qualities  attributed  to  it,  though 
attributable,  is  said  to  be  indetermined  (dSiopicn-ov,  indeter- 
minatum)  ;  it  is  only  a  possible  object  of  thought." 


CHAPTER  II. 


THE    LAWS    OF   THOUGHT. 


§  10.  The  Fundamental  Laws  of  Thought,  or  the  condi- 
tions of  the  thinkable,  are  four:  1.  The  Law  of  Identity; 
2.  The  Law  of  Contradiction  ;  3.  The  Law  of  Disjunction  ; 
and  4.  The  Law  of  Exclusion  or  Excluded  Middle. 

The  ground  of  these  Laws  is  furnished  in  the  essential 
nature  of  the  Discursive  Faculty,  or  the  Faculty  of  Thought. 
The  primitive  and  essential  gradation  in  the  operations  of 
this  faculty  is  the  Judgment.  Now  an  act  of  Judgment,  in 
its  positive  import,  is  nothing  more  nor  less  than  the  identifica- 
tion of  one  object  with  another.  When  I  affirm  or  judge,  on 
perceiving  Bucephalus,  that  he  is,  or  that  he  is  a  quadru- 
ped, I  only  identify  existence  in  the  one  case,  or  the  attribute 
of  four-footed  in  the  other,  with  Bucephalus,  as  a  part  of  the 
characters  which  make  up  the  whole  mental  object  —  Buceph- 
alus. If  I  should  affirm  all  the  attributes  which  I  recognize  in 
the  perception  as  belonging  to  him,  the  predicate  would  be 
exactly  equivalent  to  the  subject.  Such  an  affirmation  would 
be  difficult  or  impossible,  however,  in  the  case  of  an  individual 
object,  as  Bucephalus  ;  but  in  relation  to  the  object  of  thought, 
denoted  by  the  term  horse,  it  is  not  so  difficult,  as  in  the  judg- 
ment—  horse  is  a  single-hoofed,  non-ruminant  quadruped. 
In  this  judgment  the  terms  —  that  is,  the  subject,  or  that  of 
which  we  think,  and  the  predicate,  or  that  which  we  think 
of  the  subject  —  are  in  thought  exactly  equivalent,  the  impres- 
sions which  they  make  being  precisely  identical  and  indistin- 
guishable.    As  will  be  shown  hereafter,  this  judgment  may 


22  PURE  LOGIC. 

be  read  or  interpreted  in  two  ways  :  1.  In  what  is  called  its 
Comprehensive  Quantity,  thus  :  the  notion,  horse,  contains  or 
is  made  up  of  the  three  characters,  single-hoofed,  non-rumi- 
nant, quadruped.  2.  In  its  Extensive  Quantity,  thus :  the 
notion,  horse,  is  the  single-hoofed,  non-ruminant  part  of  the 
class  of  animals  called  quadruped. 

In  this  example,  the  two  terms,  the  subject  and  the  pred- 
icate, are  completely  equivalent  or  identical.  But  in  the 
more  common  class  of  judgments  the  identity  affirmed  be- 
tween the  terms  is  not  complete  or  total,  but  only  partial ;  as 
when  it  is  affirmed  the  concept,  horse,  is  single-hoofed.  In  this 
judgment  it  is  only  affirmed  that,  of  the  characters  which 
make  up  the  notion,  horse,  one  is  that  of  being  single-hoofed. 
The  identification  is  as  real  as  before  ;  but  it  is  only  partial, 
only  respects  one  of  the  plurality  of  characters  embraced  in 
the  subject. 

The  essential  nature  of  a  judgment  is  thus  an  identification, 
total  or  partial,  between  its  terms.  Hence  springs  its  one 
comprehensive  law  —  that  of  Identity.  The  force  and  im- 
port of  this  law,  is,  simply,  that  every  positive  judgment, 
to  be  a  judgment,  must  identify  —  must  affirm  an  identity  be- 
tween its  terms. 

From  this  cursory  analytic  view  of  the  nature  of  an  act 
of  thought  we  can  better  proceed  to  determine  more  exactly 
the  ground,  the  validity,  and  the  special  phases  of  the  Laws 
of  Thought,  by  a  view  of  the  manner  in  which  thought 
takes  place  in  the  mind. 

The  Reason,  under  its  specific  law  of  causality,  compels 
us  to  suppose  that  mental  activity  is  first  awakened  by  the 
presentation  of  some  object  from  without  as  its  necessary 
condition.  Let  us  suppose  this  to  be  some  impression  on 
the  sense  —  some  sensation  occasioning  a  perception.  There 
are  involved  in  this  act  two  elements,  a  mind  perceiving  and 
an  object  perceived.  The  faculty  of  Thought,  now,  from  the 
necessities  of  its  nature,  as  necessarily  self-active  when  the 
proper  conditions  of  its  acting  ax-e  brought  to  it,  recognizes 


THE  LAWS   OF  THOUGHT.  23 

these  two  terms  both  as  existing  and  also  as  different  from 
each  other.  The  idea  of  existence  is  an  idea  of  the  Reason  ;  a 
necessary,  primitive  idea.  It  is,  accordingly,  brought  in  the 
mind  face  to  face  with  each  of  the  two  factors  in  the  percep- 
tion—  the  perceiving  subject,  and  the  perceived  object. 
Thought  now,  in  the  first  place,  necessarily  affirms  this  idea 
given  by  the  Reason  —  Existence,  both  of  the  perceiving  mind 
and  of  the  external  object  —  in  other  words,  identifies  each 
of  them  as  existing.  In  the  next  place,  with  an  equal  neces- 
sity, it  affirms  that  the  perceiving  mind  is  not  the  object  per- 
ceived ;  in  other  words,  it  denies  that  they  are  identical. 
This  is  the  necessary  negative  phase  of  the  thought,  as  the 
former  is  the  necessary  positive  phase.  They  constitute  the 
two  phases  of  the  first,  comprehensive,  essential  law  of 
thought,  called  from  its  positive  phase,  the  Law  of  Identity. 

It  is  ne.cessai"ily  involved  in  this  act  of  mind  —  the  act  of 
thought,  as  it  has  now  been  regarded  —  that  to  recognize  the 
perceiving  mind  and  the  perceived  object  as  the  same  in  all 
respects,  that  is,  to  recognize  the  different  as  the  same,  to 
identify  the  non-identical,  is  the  very  contrary  of  thought  — 
is  not  thought.  In  this  view  is  founded  the  second  of  the 
Necessary  Laws  of  Thought  —  the  Law  of  Non- Contradic- 
tion, more  commonly  called  for  the  sake  of  brevity,  the  Law 
of  Contradiction. 

Still  further,  in  order  that  thought  may  thus  identify  or 
difference,  it  is  plain  there  must  be  assumed  as  the  necessary 
condition  of  its  acting  that  there  is  that  in  the  nature  of  its 
objects  which  admits  of  their  being  thus  identified  or  differ- 
enced in  thought.  In  other  words,  thought  begins  with  the 
Postulate  :  Of  all  possible  objects  of  thought,  any  two  are,  in 
respect  of  each  other,  either  the  same  or  different ;  and  so 
far  as  apprehended  at  all  in  thought  must  be  apprehended 
either  as  the  one  or  the  other  —  either  as  the  same  or  differ- 
ent. This  is  the  third  Law  of  Thought,  and  is  called  the 
Law  of  Disjunction.  The  negative  phase  of  this  law,  which 
excludes  from  thought  every  other  mode  of  apprehending  its 


24  PURE  LOGIC. 

objects,  constitutes  the  Fourth  Law  of  Thought,  called  the 
Law  of  Exclusion,  or  Excluded  Middle. 

The  first  two  laws  are  founded  immediately  in  the  nature 
of  thought ;  the  last  two,  in  the  relation  of  objects  to  thought. 
The  pairs  are  related  to  each  other  as  subjective  to  object- 
ive ;  the  two  in  each  pair  are  related  to  each  other  as  posi- 
tive to  negative. 

§  11.  The  First  General  Law  of  Thought  is  the  Law  of 
The  Law  Identity,  or  as  it  might  more  adequately  be  denom- 
of  identity.    [nate^  tfre  £aw  0f  ine  game  anc[  Different.     It 

prescribes  as  the  primary  condition  of  all  true  and  valid 
thought  that  there  ever  enter  into  it  as  its  constituents  in 
its  positive  form,  the  Same,  and  in  its  negative  form,  the 
Different.     Its  formula  is  :  a  =  a. 

This  fundamental  Law  of  Thought  has  the  characters  of 
an  Axiom.  It  validates  itself,  as  it  is  involved  in  the  nature 
of  thought.  Its  sanction  is,  that  unless  obeyed,  Thought 
cannot  be. 

The  application  of  the  law  is  universal,  and  of  like  force 
to  each  of  the  several  products  of  thought,  but,  as  will  be 
seen,  in  modes  peculiar  to  each. 

§  12.  The  Second  General  Law  of  Thought  is  the  Law 
The  Law  of  Contradiction,  or,  as  it  may  more  adequately  be 
diction.  '  denominated,  the  Law  of  Non- Contradiction.  It 
prescribes  that  the  elements  which  enter  into  any  one 
thought  be  not  thought  both  as  same  and  as  different.  Its 
formula  is  :  A  is  not  non-A,  ox  A  —  A  =  0. 

This  law  is  but  the  negative  form  of  the  First,  and  has 
the  same  self-evidencing  character  and  universal  validity  in 
Thought.  It  has  been  expressed  in  the  formula  :  Whatever 
is  contradictory  is  unthinkable.  Its  sanction  is,  that  unless 
obeyed,  Thought  is  destroyed.  Just  so  far  as  disregarded, 
just  so  far  as  the  contradictory  creeps  into  thought,  thought 
ceases  to  be  valid  —  becomes  a  zero. 

§  13.  The  Third  General  Law  of  Thought  is  the  Law 
of  Disjunction.      It  prescribes  that  when  two  objects  are 


THE   LAWS   OF  THOUGHT.  25 

presented  to  Thought,  it  recognizes  them  either  as  identical 
or  as  non-identical  —  as  the  same  or  as  different.  Its  for- 
mula is  :  A  either  is  B  or  is  not  B. 

The  ground  of  this  law  is,  as  already  indicated,  in  the 
nature  of  all  ohjects  possible  to  thought.  Thought  neces- 
sarily moves  when  the  conditions  are  supplied,  and  these 
conditions  are  the  presence  in  the  mind  of  any  two  objects  of 
thought,  necessarily  assumed  in  their  nature  either  as  same 
or  as  different.  Its  sanction  is  that,  unless  obeyed,  the  very 
conditions  of  thought  are  disowned,  and  any  act  of  thought 
is  vain  and  impotent. 

§  14.  The  Fourth  General  Law  of  Thought  is  the  Law 
of  Disjunctive  Exclusion,   also    called   Excluded  The  Law 

•     .  ,    .  .    n       „      ,  _  .  ofExclu- 

JUiddle,  and  more  briefly  Exclusion.    It  prescribes   sion. 
that  no  third  thing  be  attempted  in  thought  beyond  the  iden- 
tical and  the  non-identical,  the  same  and  the  different.     Its 
formula  is  :  A  is  not  other  than  B  or  non-B.     A  —  (B  or 
non-B)  =  0. 

This  law  is  the  prohibitory  or  negative  side  of  the  Law 
of  Disjunction.  Like  that,  it  is  grounded  on  the  essential 
nature  of  things  as  possible  to  thought.  Its  sanction  is  that, 
unless  obeyed,  the  Faculty  of  Thought  departs  from  its 
sphere,  and  its  movements  are  invalid  and  illusory. 

The  Third  and  the  Fourth  Law  stand  in  the  same  relation 
to  each  other  as  the  First  and  the  Second,  constituting  like 
them  a  Duad  composed  of  two  elements,  a  Positive  and  a 
Negative. 

The  first  Duad,  the  Laws  of  Identity  and  Contradiction, 
indicate  the  positive  or  actual  characters  of  all  true  Thought ; 
they  are  the  Subjective  Laws  of  Thought.  The  second, 
those  of  Disjunction  and  Exclusion,  express  the  predeter- 
mining conditions  of  all  actual  thought  ;  they  are  the  Ob- 
jective Laws  of  Thought. 

§  15.   From  what  has  been  said  in  respect  to  the  nature 
of  thought,  it  appears  that  in  every  thought  there   Relations 
are  two  terms  or  factors  ;  as  when  I  think  Bu-    —^uldTol 
cephalus   as   existing,    there    are    the  two  terms   wholes- 


26  PURE  LOGIC. 

Bucephalus,  and  Existing.  They  are  parts  of  the  thought. 
This  judgment  is  thus  a  Whole  in  relation  to  the  terms,  and 
the  terms  are  complementary  to  each  other.  If  I  think  at 
all  of  any  subject,  I  must  think  some  predicate  of  it ;  so  if  I 
think  of  any  predicate,  I  must  think  some  subject.  In  every 
thought,  accordingly,  is  necessarily  the  double  relationship, 
that  of  Whole  and  Parts,  and  that  of  Parts  which  are  com- 
plementary of  each  other — the  relation  of  Quantity.  As 
the  thought  takes  in  more  subjects  or  more  predicates,  be- 
comes more  composite,  the  Quantity  becomes  increased,  and 
the  relationships  between  the  parts  are  multiplied,  without, 
however,  destroying  or  obliterating  the  primitive  duality 
which  characterizes  all  thought.  Instead  of  one  part  being 
exactly  complementary  of  another  part,  it  may  be  but  jointly 
with  others  so  complementary  —  partly  complementary  of  it. 
All  proper  thought,  however  complicated,  being  essentially 
founded  on  this  one  principle  of  Identity,  thus  of  its  own 
nature  unfolding  itself  into  all  the  complications  of  Quantity, 
or  the  manifold  relations  of  Whole  to  all  or  any  one  of  its 
Parts,  and  of  a  Part  to  any  one  or  more  complementary 
Parts,  it  becomes  necessary  to  present  here  a  summary  view 
of  the  different  kinds  of  Wholes  which  exact  and  effective 
thought  requires  should  be  readily  discriminated.  This  will 
be  done  in  the  next  chapter. 


CHAPTER  III. 

THE   WHOLES  IN  THOUGHT.  —  LOGICAL  POSTULATE. 

§  16.  Wholes  may  first  be  divided  into  two  genera  —  into 

I.  A  Whole  by  itself,  (totum  per  se)  ; 

II.  A  Whole  by  accident,  (totum  per  accidens). 

I.  Of  the  first  kind  of  Wholes,  there  are  Five   (a)  whole 
Species:  byitself- 

1.  The  Whole  of  Thought  —  the  Dlanoetic  Whole.  Every 
thought  includes  a  positive  and  a  negative.  If  we  -j  Dianoetic 
think  explicitly  A  is  B,  we  also  think  implicitly   Wk°le- 

A  is  not  11011- B.    The  two  make  up  the  whole  of  the  thought 
in  the  relation  of  A  to  B. 

2.  The    Whole   of  the   necessary  Forms  in   which  Being 
enters  into  thought  —  the  Integrate  or  Maihemat-  %  integrate 
ical  Whole.     This  species  has  two  varieties  :  (1.)    ematicai" 
The  Numerical,  or  that  of  Time.     (2.)   The  Geo-  AVtole- 
metrical,  or  that  of  Space.     As  applied  to  Bodies  in  Time 
and  Space,  these  become  respectively  Collective  and  Mass 

Wholes ;  a  Collective  Whole  being  constituted  of  parts  nu- 
merically different  from  one  another,  as  a  heap  of  stones,  a 
forest  of  trees;  a  Mass  Whole  being  constituted  of  parts  spe- 
cially different  from  one  another,  as  a  gallon  of  water,  a  block 
of  wood.  In  this  kind  of  Whole,  the  Mathematical  or  Inte- 
gral, the  parts  lie  out  of  one  another,  and  their  relation  to 
the  Whole  is  expressed  by  the  preposition  of. 

3.  A  Whole  of  Being  —  an   Essential    Whole.     This  in- 
cludes two   species :  (1.)   A  Whole  of  Substance,  3  ■Es3m. 
composed  of  substance  and  attributes  —  a  Substan-  tiai  Wh°l6- 
tial  Whole.     (2.)  A  Whole  of  Cause,  composed  of  Cause  and 


28  PURE  LOGIC. 

its  Effects  —  a  Causal  Whole.  Substance  and  Attribute  on  the 
one  hand,  and  Cause  and  Effect  on  the  other,  are  respective- 
ly complementary  of  each  other  in  our  thought,  so  that- we 
cannot  think  the  one  without  thinking  the  other;  just  as  we 
cannot  think  a  positive  without  thinking  a  negative  in  a  Dia- 
noetic  Whole,  or  a  part  of  a  Mathematical  Whole,  as  the  half 
of  a  number,  or  the  half  of  a  surface,  without  thinking  the 
other  half. 

4.  A  Logical  Whole,  being  the  artificial  whole  of  the  Dis- 
4  Logical  cursive  Faculty,  embracing  the  two  species  of 
Whole.  i.  The  Extensive  Whole,  or  the  Whole  of  Extension. 

which  is  the  whole  of  the  objects  embraced  under  a  notion, 
2.  The  Intensive  or  Comprehensive  Whole,  or  Whole  of  Com- 
prehension, which  is  the  whole  made  up  of  the  characters  or 
attributes  that  make  up  a  notion. 

Thus  the  notion  man  is  regarded  as  a  whole,  containing 
two  kinds  of  parts.  One  kind  of  parts  enbraces  such  as  the 
varieties  —  Asiatic,  African,  European,  American,  or  the  in- 
dividuals that  make  up  the  race.  The  notion  is  then  said  to 
be  taken  in  its  Extensive  Quantity,  or  the  Quantity  of  In- 
tension. It  is  an  Extensive  Whole.  The  other  kind  of 
parts  includes  such  as  Rational,  Animal,  Intelligent,  Suscep- 
tible, Moral.  The  notion  is  then  said  to  be  taken  in  its  Com- 
prehensive or  Intensive  Quantity  or  the  Quantity  of  Compre- 
hension.    It  is  an  Intensive  or  Comprehensive  Whole. 

When  a  notion  is  taken  in  Extensive  Quantity,  it  is  said 
to  contain  its  parts  under  it.  As  the  whole  man  taken  exten- 
sively contains  under  it  the  parts  Asiatic,  African,  European, 
American,  Socrates,  Plato,  Demosthenes,  Ccesar,  &c.  Or  if 
the  part  be  made  the  subject,  the  parts,  Asiatic,  &c,  are  con- 
tained under  the  whole,  man.  Such  parts  are  called  Exten- 
sive Parts. 

When,  on  the  other  hand,  a  notion  is  taken  in  Comprehen- 
sive Quantity,  it  is  said  to  contain  its  parts  in  it.  Thus,  the 
whole,  man,  taken  comprehensively,  contains  in  it  the  attri- 
butes or  characters  Rational,  Animal,  Intelligent,  Suscejytible, 


THE  WHOLES   IN  THOUGHT.  29 

Moral ;  or  the  characters  Rational,  &c,  are  contained  in  the 
notion,  man.  Such  parts  are  called  Intensive  or  Comprehen- 
sive Parts. 

This  kind  of  Wholes  is  called  Logical,  because  they  are 
thought  Wholes;  that  is,  they  are  Wholes  constructed  by  the 
mind  for  its  own  convenience  and  use,  and  not  necessarily 
actual  wholes.  The  mind  can  construct  as  many  of  these 
kinds  of  Whole  as  it  finds  necessary ;  and,  although  its  classi- 
fications will  be  founded  on  correspondencies  in  the  actual 
world,  at  least,  will  not  designedly  contradict  them  ;  yet  they 
are,  in  number  and  in  kind,  determined  not  by  the  actual,  but 
by  the  conveniencies  of  science  or  knowledge. 

As  will  appear  hereafter,  an  Extensive  Whole  is  composed 
of  the  subjects  of  Judgments,  and  a  Comprehensive  Whole  of 
the  predicates  of  Judgments. 

5.  A  Corporate  or  Representative  Whole,  called  also,  and 
more  properly  a  Formal  or  ^Esthetic  Whole,  is  made   5   Corpor. 
up  of  the  matter  and  the  form  in  every  individual   ate  ^holes- 
object  of  imagination,  or  more  exactly,  and  more  comprehen- 
sively, it  is  a  Whole  made  up  of  idea,  and  the  matter  in  which 
the  idea  is  embodied. 

§  17.     II.  Wholes   bt  Accident   include   such  as  the 
relative  Whole  of  Degree,  as,  Mankind  is  made  up    (bj  y^^^ 
of  the  poor  and  the  rich  ;  of  Position,  as  northern    b^  Accident- 
and  southern  ;  of  Affinity,  as  parent  and  child,  and  the  like. 

§  18.  "The  only  postulate  of  Logic  which  requires  an 
articulate  enouncement,  is  the  demand  that  before   The  Logic- 

al   Postu- 

dealing  with   a  judgment,  concept,  or  reasoning,    late, 
expressed  in  language,  its  import  should  be  fully  understood  ; 
in  other  words,  Logic  postulates  to  be  allowed  to  state  ex- 
plicitly in  language  all  that  is  implicitly  contained  in  the 
thought. 

This  postulate  can  not  be  refused.  In  point  of  fact,  Logic 
has  always  proceeded  on  it,  in  overtly  expressing  all  the 
steps  of  the  mental  process  in  reasoning  —  all  the  proposi- 
tions of  a  syllogism ;  whereas,  in  common  parlance,   one   at 


30  PURE  LOGIC. 

least  of  these  steps  or  propositions  is  usually  left  unex- 
pressed. This  postulate,  though  a  fundamental  condition  of 
Logic,  has  not  been  consistently  acted  on  by  logicians  in 
their  development  of  the  science  ;  and  from  this  omission 
have  arisen  much  confusion  and  deficiency  and  error  in  our 
present  system  of  Logic.  Aristotle,  however,  states  of  syl- 
logistic—  and,  of  course,  his  statement  applies  to  Logic  in 
general  —  that  the  doctrine  of  syllogism  deals,  not  with  the 
external  expression  of  reasoning  in  ordinary  language,  but 
with  the  internal  reasoning  of  the  mind  itself." 


CHAPTER  IV. 

THE  PRODUCTS  OF  THOUGHT.  —  1.  JUDGMENTS. 

§  19.  The  primitive  and  essential  gradation  of  thought 
we  have  indicated  to  be  the  Judgment.  In  accordance  with 
what  has  been  said,  a  Judgment  may  be  defined  to  be  a  rec- 
ognition of  the  identity  or  non-identity  between  Jud„ment 
any  two  objects  presented  to  the  Faculty  of  Thought.  deflned- 
As  expressed  in  words,  a  Judgment  is  called  a  Proposition, 
or  in  grammatical  nomenclature,  a  Sentence. 

Besides  the  Judgment,  there  are  two  other  products  of 
thought,  both  derivatives  from  the  Judgment.  The  one  is 
the  Concept,  which  is  derived  from  several  Judgments  by  an 
act  of  Conceiving —  taking  together,  in  other  words,  by  an  act 
of  synthesis.  The  other  is  the  Reasoning,  which  is  derived 
from  one  or  more  Judgments  by  an  act  of  analysis  or  sepa- 
ration. As  all  thought  is  essentially  a  movement  in  Quan- 
tity, and  as  variations  in  Quantity  can  be  effected  only  in  the 
one  or  the  other  of  these  two  directions,  synthesis  and  anal- 
ysis, the  Concept  and  the  Reasoning  are  the  only  conceivable 
derivatives  from  a  Judgment,  except  such  as  consist  only  in 
variations  of  form,  that  do  not  affect  the  identity  of  the 
thought. 

In  explication  of  this  definition  of  a  Judgment,  it  will  be 
necessary  simply  to  recall  what  has  been  already  said  in  the 
exposition  of  the  general  nature  of  thought.  As  we  have 
seen,  a  judgment  necessarily  supposes  two  objects  ;  and  its 
essential  characteristic,  as  an  act  of  Intelligence,  consists  in 
this :  that  it  is  a  cognition  of  this  particular  relation  of  iden- 
tity or  non-identity  between  the  two  objects.     These  two 


32  PURE  LOGIC. 

objects  of  a  judgment  are  given  to  it  by  some  other  faculty 
of  the  Intelligence,  as  of  Perception,  Intuition,  Memory,  or 
by  the  Discursive  Faculty  itself,  in  some  previous  exercise. 
It  may  be  some  object  of  Perception,  as  Bucephalus.  As 
thus  given  by  the  Perceptive  Faculty,  the  cognition  is  of  an 
object  by  itself,  without  relation  either  to  other  objects  or  to 
the  parts  of  the  object  itself.  Color  is  not  in  the  perception 
itself  distinguished  from  figure  ;  neither  color  nor  figure  from 
the  position  or  the  time  in  which  it  is  perceived ;  and  neither 
of  these  from  the  useful  qualities  of  the  object.  All  the  per- 
ceptible qualities  are  given  together  without  distinction  in  the 
presentation  itself  of  the  object.  But  when  thus  given,  the 
mind  at  once,  and  by  a  kind  of  necessity  of  its  being  as  essen- 
tially active  and  reflective,  exerts  its  activity  on  it,  first,  by 
apprehending  it  as  a  part  of  a  multiplicity  of  objects  around, 
to  each  of  which  it  stands  in  relation,  and  also,  as  a  whole, 
containing  parts  in  itself.  This  is  the  primitive  and  condi- 
tional gradation  in  all  thought  —  the  apprehension  of  an 
object  as  a  part  or  as  a  whole  —  in  other  words,  in  the  rela- 
tion of  Quantity.  Simultaneously  with  this,  it  apprehends 
some  other  object  of  thought  given  to  it  by  Perception,  or 
by  some  other  Faculty  of  the  Intelligence,  or  in  some  pre- 
vious exercise  of  the  Judgment,  and  thus  comes  to  view  the 
two  objects  thus  given  in  relation  to  each  other,  as  the  same  . 
or  not  the  same.  Its  act  then  becomes  complete  ;  and  a  per- 
fected product  of  thought,  a  Judgment,  is  the  result.  Thus 
the  second  object  may  be  given  in  the  Perception  itself,  as 
black,  or  four-footed,  and  the  Judgment  recognizes  this  color 
or  this  form  as  belonging  to  Bucephalus  —  that  is,  as  iden- 
tical with  one  of  the  parts  or  characters  that  make  up  the 
whole  perception.  Or  the  second  object  may  be  given  by 
the  Regulative  Faculty,  or  Faculty  of  Intuition,  as  of  Being, 
of  Space,  of  Time,  or  other  idea  of  the  proper  Reason  ;  and 
then  the  Judgment  identifies  Bucephalus  with  Existence,  with 
some  part  of  Space,  of  Time ;  or  in  other  words,  affirms 
Bucephalus  to  be,  to  be  in  such  a  place,  at  such  a  time,  and 


JUDGMENTS.  33 

the  like.  The  second  object  of  thought  may,  in  like  manner, 
be  given  to  the  Judging  Faculty  by  the  Memory.  We  may 
identify  Bucephalus  as  now  perceived  with  the  Bucephalus 
perceived  yesterday  ;  with  the  black  color,  the  four-footed 
figure,  before  perceived  in  some  other  object. 

The  essential  nature  of  a  Judgment,  thus,  is  seen  to  be  an 
identification  of  one  object  with  another,  either  totally  or  par- 
tially—  in  some  on£  or  in  all  respects.  It  is  accordingly  a 
relative  cognition  ;  and  in  the  relation  which  it  involves  are 
necessarily  contained  three  elements :  1.  The  object  of 
thought  identified  with  some  other.  2.  The  object  with 
which  it  is  identified,  either  in  whole  or  in  part.  And,  3. 
The  mental  act  which  identifies.  The  first  two  constitute 
the  matter  of  thought,  the  datum  ;  the  last  is  the  Thought 
itself,  the  identifying  cognition  —  the  Judgment. 

§  20.  To  the  several  parts,  or  to  different  aspects  of 
the  complex  procedure  in  all  Thought  as  thus  exemplified  in 
one  of  its  gradations  —  the  Judgment  —  Psychology  has  as- 
signed distinctive  names,  which  it  may  not  be  inexpedient 
here  to  recall. 

Inasmuch  as  the  original  datum  or  object  of  thought  is 
given  in  an  indefinite  vagueness  as  one  and  undi- 
vided, and  as,  in  order  to  be  cognized  in  thought,      na  ys1' 
it  must  be  viewed  in  relation  to  some  part,  it  becomes  neces- 
sary to  loosen  up,  to  analyze  or  separate  it  as  a  whole  into 
its  parts.     This  part  of  the  process  is  called  Analysis. 

The  next  step  is  to  select  the  part  out  of  the  whole  for  sepa- 
rate apprehension,  and  to  draw  it  away,  as  it  were,  to  ab- 
stract it  from  the  other  parts.  This  part  of  the  movement 
in  Thought  is  called  Abstraction.     The  term,  how- 

...  ii-  t    i  •  •  Abstraction. 

ever,  it  is  proper  to  add,  is  applied  in  various  ways 
by  different  writers  or  on  different  occasions,  but  with  the 
same  result.  Thus  it  may  be  applied  to  the  mind  itself;  so 
that  in  Abstraction  the  mind,  when  confining  its  view  to  cer- 
tain parts  of  an  object,  is  regarded  as  being  abstracted  or 
drawn  away  from  the  parts  that  are  to  be  excluded  from 
3 


34  PURE  LOGIC. 

view ;  and  this,  it  may  be  observed,  is  in  strictness  the  most 
correct  view.  But  in  a  looser  sense  the  term  may  be  applied 
to  the  part  itself  that  is  selected,  and  then  such  part  is  re- 
garded as  being  abstracted  from  the  other  parts.  Or,  in  the 
third  place,  it  may  be  applied  to  those  other  excluded  parts 
themselves,  and  then  they  are  regarded  as  being  abstracted 
or  drawn  away  either  from  the  other  parts  or  from  the  mind's 
consideration.  The  result  is  the  same  in  any  view,  that  one 
part  is  separated  from  the  other  parts  for  exclusive  consider- 
ation, and  it  is  therefore  a  matter  of  indifference,  so  far  as  the 
result  is  concerned,  which  of  these  different  views  is  enter- 
tained. 

When  thus  one  part  is  separated  from  the  rest  for  exclu- 
sive consideration  by  the  mind,  the  act  of  mind  in 

Attention.  . 

which  it  concentrates  its  notice  upon  it  is  called 
Attention. 

In  the  next  place,  the  two  objects  are  brought  up  and 
viewed  face  to  face  with  each  other  in  order  that  their  iden- 
tity or  non-identity  may  be  apprehended.  This  part  of  the 
process  is  called  Comparison. 

Finally,  the  last  part  of  the  complex  process,  in  which  the 
thought  is  perfected  by  bringing  together  the  two 
objects  attended  to  into  one  relative  cognition,  is 
called  an  act  of  Synthesis. 

All  Thought  thus  begins  with  an  Analysis,  it  proceeds  by 
Abstraction,  Attention,  and  Comparison,  it  ends  with  a  Syn- 
thesis. And  this  is  to  be  understood  in  a  sense  more  or  less 
full  and  complete,  in  modes  varying  with  the  nature  of  the 
particular  gradation  of  all  the  acts  of  thought,  whether  *n 
judging,  conceiving,  or  reasoning.  The  two  essential  elements 
of  thought  are  analysis  and  synthesis.  With  one  it  neces- 
sarily begins,  with  the  other  it  necessarily  ends.  For  its  very 
function  is  to  lead  to  truth,  to  a  unity  in  the  intelligence, 
which  supposes  an  undistinguished  manifold  as  its  condition, 
and  a  gathering  into  a  unity  as  its  result.  The  other  parts 
of  the  complex  process,  abstraction,  attention,  and  compari- 


JUDGMENTS.  35 

son,  are  the  means  by  which  the  mind  passes  from  the  mul- 
tiform given  in  the  analysis  to  the  unity  in  the  synthesis. 

Inasmuch  as  in  a  Judgment  an  object  is  regarded  only  in 
one  of  manifold  relations,  the  act  is  appropriately  called  a 
determination  of  the  object  —  a  limiting  down  to  some  speci- 
fied relationship.  And,  accordingly,  the  object  which  is  iden- 
tified with  another  is  called  the  determined  element  of  the 
judgment,  and  that  with  which  it  is  identified,  is  called  the 
determining  element. 

§  21.  Of  the  two  objects  of  thought  identified  in  a  Judg- 
ment, one  is  necessarily  viewed  as  the  primitive  partS0fa 
which  is  to  be  identified  with  the  other,  or  is  deter-  Judsmenr- 
mined  by  it.  This  so  viewed  primitive  or  determined  object 
is  called  the  Subject ;  which  may  be  defined  to  be  that  of 
which  we  judge.  The  other,  viewed  as  the  determining  ele- 
ment, is  called  the  Predicate,  which  may  be  defined  to  be  that 
which  is  judged  of  the  subject.  The  Subject  and  the  Predi- 
cate make  up  the  matter  of  thought  or  the  datum  to  thought. 
They  are  called  the  Terms  of  a  Proposition,  {termini,  opoi.) 
The  act  of  thought  itself  which  recognizes  the  identity  be- 
tween the  two  terms  is  called  the  Copula,  which  may  be  defined 
to  be  the  identification  of  two  objects  of  thought.  It  was 
called  by  Aristotle,  in  reference  to  the  two  terms,  an  Interval, 
(SiaoT?7/xa). 

Thus,  in  the  proposition,  iron  is  magnetic,  we  have  iron 
for  the  Subject,  magnetic  for  the  Predicate,  and  is  for  the 
Copula.  It  is  not  always  the  case,  however,  that  in  proposi- 
tions the  copula  is  expressed  by  is,  or  in  a  distinct  word  from 
the  predicate. 

In  fact  the  copula  is  expressed  separately  thus  only  when 
the  subject  is  apprehended  as  substance  and  the  Judgment 
identifies  one  of  its  parts  as  a  quality.  As  in  the  example, 
iron  is  magnetic,  the  meaning  is  that  one  of  the  qualities  of 
the  subject,  iron,  is  the  quality  magnetic  —  iron,  in  one 
respect,  is  magnetic,  the  identification  being  partial.  But  in 
the  proposition,  iron  magnetizes,  the  subject,  iron,  is  appre- 


36  PURE  LOGIC. 

hended  as  cause.  In  this  expression  the  copula  is  merged  in 
the  predicate.  In  the  English  Language  there  are  no  longer 
verba  expressing  simply  quality,  like,  perhaps,  the  Latin 
albet,rubet,  and  as  in  the  obsolete  English  of  Wickliffe,  "  Thou 
maddist."  They  all  express  action,  and  require  that  the  sub- 
ject be  apprehended  as  cause.  And  the  meaning  of  the 
proposition,  iron  magnetizes,  is  that  it  identifies  a  part  of  the 
causal  agency  of  iron  with  magnetizing.  Here,  also,  the 
identification  is  partial.  There  is,  perhaps,  one  exception  to 
this  general  remark  in  regard  to  English  verbs.  The  so- 
called  substantive  verb,  to  be,  is  used  often  to  express  the 
quality  of  Existence,  as :  God  is  ;  there  is  a  God.  There 
are  manifold  other  ways  of  expressing  the  copula,  which 
will,  so  far  as  necessary,  be  indicated  hereafter. 

§  22.  The  word   Term,  as  used   technically  in  Logic,  it 
The  Terms      should  be  observed,  is  applied  either  to  the  sub- 

ofaJudg-  .  . 

ment.  ject  or  to  the  predicate  of  a  proposition.     It  may 

embrace  one  or  more  principal  notions ;  thus  in  the  proposi- 
tion, The  greatest  vicissitude  of  things  among  men  is  the 
vicissitude  of  sects,  there  are  three  principal  notions  or 
objects  of  thought  in  the  subject,  vicissitudes,  things,  men  ; 
but  with  the  other  modifying  and  relative  words  they  make 
but  one  logical  Term.  So  the  predicate  contains  two  notions 
or  objects  of  thought.  In  a  single  proposition,  there  can  be 
but  two  Terms  —  one  subject  and  one  predicate.  In  a  com- 
pound proposition  there  are,  of  course,  as  many  Terms  as 
there  are  distinct  subjects  affirmed  of,  and  distinct  predicates 
affirmed.  In  the  proposition,  James  and  John  are  related, 
there  is  but  one  affirmation,  one  subject,  one  predicate,  and, 
accordingly,  two  Terms.  In  the  proposition,  James  and  John 
are  learned  and  virtuous,  there  are  distinguishable  four 
affirmations,  four  subjects,  four  predicates,  and  eight  Terms, 
inasmuch  as  it  may  be  decomposed  into  the  four  single  prop- 
ositions: Jams  is  learned,  John  is  learned,  James  is  virtuous, 
John  is  virtuous.  It  should  be  added  that  the  judgment 
may  be  compounded  of  two  or  more  copulas. 


JUDGMENTS.  37 

The  Terms  of  a  Judgment  are  ever  to  be  viewed  as  objects 
of  thought.  Even  when  a  Term  is  presented  as  an  original 
primitive  datum  by  another  Faculty,  as  the  Perceptive,  and 
so  far  as  thus  given,  affords  only  a  simple,  irrelative  cogni- 
tion, so  soon  as  it  is  accepted  by  the  Faculty  of  Thought,  it 
assumes  a  new  character;  it  is  no  longer  simple,  but  a  rela- 
tive cognition.  Thus  in  the  judgment,  Bucephalus  is  four- 
footed,  the  subject,  Bucephalus,  is  in  the  thought  appre- 
hended either  as  an  individual  —  as  one  of  many  four-footed 
things  ;  as  a  part  of  a  whole  —  or  as  a  whole  containing  one 
of  many  parts,  which  here  are  attributes  or  characters,  as 
that  of  four-footed,  that  is,  as  one  of  many  other  attributes 
that  belong  to  Bucephalus  as  a  substance. 

As  objects  of  thought,  the  Terms  of  a  Judgment  are  thus 
ever  cognitions,  not  real  objects.  In  the  Judgment,  Buceph- 
alus is  four-footed,  the  subject  is  Bucephalus,  as  known,  as 
already  introduced  into  the  mind  by  the  Perceptive  Faculty, 
and  entertained  there  not  as  actual,  but  only  as  known. 
This  observation  has  been  made  sufficiently  prominent,  per- 
haps, in  the  exposition  already  given  of  the  nature  of 
Thought ;  but  it  cannot  well  be  too  forcibly  impressed  on  the 
mind,  in  the  study  of  the  elements  of  thought,  that  they  are 
all  cognitions;  and  not  only  that,  but  they  are  also  all  essen- 
tially relative  cognitions.  A  Term,  thus,  is  not  a  simple 
representation,  as  Hamilton  seems  to  teach,  but  a  relative 
cognition,  partaking  at  once,  as  soon  as  accepted  by  though^ 
of  the  relativeness  that  is  characteristic  of  all  thought. 

The  Terms  of  a  judgment  may  be  conveniently  distrib- 
uted into  three   classes,   distinguished  by  the  re-   Terms  of 

.  ,  .    .        ,  ,  ,  three  grades 

epective  modes  in  which  they  are  thought,  or  or  classes. 
more  exactly,  by  the  different  stages  at  which  they  are 
respectively  accepted  as  objects  in  the  elaborative  process 
bestowed  by  thought  on  the  original  datum.  At  the  first 
stage  is  this  primitive  datum  itself,  as  accepted  from  the 
Perceptive  or  Intuitive  Faculties,  and  invested  with  the 
character  of  relativeness   attaching  to  all  thought ;  of  this 


38  PURE  LOGIC. 

class  are  all  individual  and  simple  cognitions,  as  Bucephalus, 
Mars,  Socrates,  Space,  Time,  Being,  Identical,  and  the  like. 
At  the  next  stage  are  the  products  of  a  synthesis  of  these 
terms  of  the  first  class,  to  be  hereafter  more  fully  described, 
called    Concepts,  which,  as  modified  or  not,   make  up  the 
larger  part  of  the  Terms  used  in  discourse. 
•  At  the  third  stage  are  Judgments   themselves  used  as 
Terms  in  other  Judgments ;  as,   That  men  are  free  is  a  doc- 
trine of  general  recognition  ;  If  virtue  is  voluntary,  vice  is 
voluntary.     A  Judgment  thus  used  as  a  Term  is  called  a 
Clause.     That  men  are  free,  is  thus  a  Clause. 

§  23.     Besides  the  Terms,  —  the  Subject  and  the  Predi- 
The  copula     cate,  —  as  we  have  seen,  there  is  another  element 
mentU  S*      in  the  Judgment,  namely,  the  Copula,  a  reciprocal 
relation  between  these  Terms  as  determining  and  determined. 
This  is  the  pure  Thought-element.      It  is  important  here 
to  investigate  its  precise  nature   or   character.     We  have 
already  found  that  all  thought   is   relative  —  that   it   ever 
proceeds  under  the  relations  of  Quantity.     Now  there  are 
two   kinds    of  relationship,    equally   primitive   and  equally 
necessary,  involved  in  this  general  relation  of  Whole  and 
Parts.      There  is  first  the  relation  of  Whole  to  Part,  with 
its  converse  of  Part  to  Whole.     There  is  next,  the  relation 
of  Part  to  Part ;  as  we  cannot  think  a  Part  without  thinking 
its  Complementary  Part.    These  two,  then,  are  the  primitive 
channels  of  thought,  inasmuch  as  it  moves  ever  between  the 
Whole  and  the  Part,  or  between  the  Part  and  the  Complement- 
ary Part.     The  Copula  determines  indifferently  in  either  of 
these  two  relations.     It  identifies  the  Whole  as  containing  the 
Part,  and  identifies  one  Part  as  complementary  of  the  other. 
This  is  its   positive  form.     It  denies,  however,  as  well  as 
affirms  ;  it  differences  as  well  as  identifies.     Accordingly  in 
one  relation  it  differences  in  one  view  the  Whole  from  the 
Part,  as  well  as  in  another  view  it  identifies  them  ;  and  in 
the  other  relation,  it  differences  the  one  Part  from  the  Com- 
plementary Part  in  one  view,  as  in   another  it  identifies 
them.     This  is  the  negative  form  of  thought. 


JUDGMENTS.  39 

Language  furnishes  modes  of  Expression  for  marking  these 
diverse  movements  of  thought  in  the  Copula.  It  represents 
the  relation  of  Whole  and  Part  by  such  terms  as  contains, 
comprehends,  comprises,  and  the  like ;  while  it  represents  the 
relation  recognized  between  Part  and  Part,  by  such  words 
as  implies,  involves,  and  the  like.  The  words,  determine, 
condition,  and  others  also  express  the  Copula  in  its  various 
relations. 

In  that  stricter  analysis  of  thought  and  expression  which 
is  necessary  in  the  training  of  the  mind  to  accurate  thinking 
and  representation,  and  which  is  also  required  for  the  criti- 
cal examination  of  discourse,  this  diverse  mode  of  determin- 
ing in  thought,  and  of  expressing  the  determination  in  lan- 
guage, needs  to  be  familiarly  known.  It  will  of  course  be 
understood  that  such  expressions  as  Virtue  is  Free,  or  Vir- 
tue contains  Freedom,  and  Virtue  implies  Vice,  when  inter- 
preted in  their  proper  logical  significance,  mean :  Virtue  in 
one  of  its  parts  is  identical  with  Freedom ;  and  Virtue  is 
identical  with  Vice  in  some  one  respect,  that  is,  as  being 
free. 

§  24.  Judgments  may  be  distributed  into  different  sets 
of  species,  on  several  distinct  principles  of  divis-  DiTisi0D  of 
ion.  As  a  judgment  is  made  up  of  internal  Judgments. 
form  and  matter,  of  thought  proper,  which  is  a  purely 
subjective  element,  and  the  datum  to  thought,  which  is  a 
purely  objective  element,  the  former  of  which  constitutes  the 
copula  and  the  latter  the  terms  of  the  judgment,  we  should 
anticipate  finding  in  each  of  these  constituents  of  all  thought, 
one  or  more  grounds  of  distinction.  And  accordingly,  look- 
ing first  to  the  subjective  element,  the  copula,  we  find  that 
there  are  three  different  principles  of  division  given  in  it. 

First,  the  judgment  may  vary  in  respect  to  its  own  inter- 
nal and  essential  nature  and  irrespectively  of  its  *j  ^/co*-0* 
necessary  relations  to  its  matter  and  expression.    ula- . 

J  .  r  .        (1.)  As  to  its 

This  is  the  proper  quality  of  a  judgment;  and  in   Quality. 


40  PURE  LOGIC. 

respect  to  its  Quality,  as  we  have  seen,  while  a  Judgment 
may  be  affirmative  or  negative,  it  must  be  one  or  the  other. 
Strictly  speaking,  the  necessity  of  judging,  when  two  objects 
of  thought  are  given,  either  that  they  are  or  that  they  are 
not  identical,  is  imposed  upon  the  Faculty  of  Thought  as  a 
pre-determining  condition,  as  the  objective  Law  of  Thought ; 
while  its  own  proper  function  lies  in  taking  the  one  or  the 
other  of  these  alternatives  —  of  affirming  or  denying.  We 
may  accordingly  ground  the  first  division  of  Judgments  on 
their  essential  Quality.  This  distinction  will  give,  1.  The 
simple  Affirmative  and  Negative;  2.  The  Disjunctive;  —  the 
first  being  grounded  on  the  Subjective  Laws  of  Identity  and 
Contradiction  ;  the  second  on  the  Objective  Laws  of  Disjunc- 
tion and  Exclusion.  The  first  may  be  distinguished  as  of  Sim- 
ple Quality ;  the  last  as  of  Disjunctive  Quality.  Further,  the 
first  named  species  move  more  freely  and  characteristically 
in  the  relation'  of  Whole  and  Part ;  the  second  in  that  of 
Part  and  Complementary  Part. 

Secondly,  the  Judgment  may  be  combined  or  not  with  a 
(2  )  its  Mo-  recognition  of  the  ground  of  its  determination.  If 
daiity.  n0(;  so  combined,  the  Judgment  is  pure,  simple,  or 

unmodified.  It  is  then  denominated  an  Assertory  Judgment, 
as  it  is  a  mere  assertion  unmixed  with  any  extraneous  ele- 
ment. But  the  Judgment  may  take  up  with  itself  into  the 
same  act  of  consciousness  the  ground  of  its  determination  ; 
it  thus  becomes  so  far  modified.  It  is  then  denominated,  in 
distinction  from  the  pure  or  unmodified  —  that  is,  in  distinc- 
tion from  the  Assertory  Judgment  —  a  Modal  Judgment. 

This  principle  of  distinction  in  Judgments  is  what  is  known 
as  the  Modalily  of  Judgments. 

The  Assertory  Judgment,  it  is  obvious,  cannot  be  further 
subdivided  in  respect  to  this  principle.  '  But  the  Modal  Judg- 
ment can  be  still  further  distinguished  in  respect  to  the  par- 
ticular grounds  that  may  be  recognized  by  the  Judgment  in 
its  determination.  These  grounds  may  either  lie  wholly 
within  the  sphere  of  thought,  or  out  of  it,  that  is,  in  the 


JUDGMENTS.  41 

matter,  the  datum  of  thought.  If  the  ground  of  the  Judg- 
ment be  recognized  as  lying  wholly  within  the  sphere  of 
thought,  then  there  emerges  the  Necessary  or  Apodictic 
Judgment.  If  the  ground  of  the  Judgment  be  recognized, 
and  as  lying  not  in  the  thought,  but  in  the  matter  of  the 
thought,  then  emerges  the  Contingent  or  Problematic  Judg- 
ment. 

There  may  obviously  be  distinguished  subdivisions  of  the 
Problematic  Judgment.  The  higher  grades  of  these  subdi- 
visions, indicated  by  such  modals  as  probably,  possibly,  are, 
not  unsuitably,  recognized  in  Logical  Science.  Aristotle  in 
his  Treatise  on  Interpretation,  enumerates  four  kinds  of  prop- 
ositions grounded  on  their  modality :  Possible,  Contingent, 
Impossible,  and  Necessary.  In  his  Prior  Analytics,  he 
speaks  only  of  the  Necessary  and  the  Contingent  in  distinc- 
tion from  Pure  Propositions.  These  three  primary  distinc- 
tions are  all  that  it  seems  important  to  notice  here. 

The  characters  of  Judgments  that  are  determined  by  this 
principle  of  modality,  which  respects  the  grounds  on  which 
the  Judgment  is  recognized,  should  be  carefully  distinguished 
from  such  characters  as  those  of  clear,  vague,  obscure,  which 
only  look  to  the  degree  of  consciousness,  the  mental  force  or 
energy  involved  in  the  Judgment. 

It  may  further  be  observed,  that  the  character  of  neces- 
sary helongs  properly,  that  is,  primarily  and  strictly,  only  to 
that  truth  or  certainty,  the  ground  of  which  lies  in  the 
thought  itself  exclusively.  Thought  must  ever  accept  its 
own  product  as  valid  and  beyond  question  ;  while  all  beyond 
that,  even  its  own  product  so  far  as  combined  with  matter  which 
is  not  of  pure  thought,  it  must  ever  hold  as  not  necessary, 
only  problematical.  Only  the  contradictory  of  pure  thought 
can  be  called  absurd  in  the  highest  sense.  As  thought  orig- 
inates cognitions,  which  cognitions  may  themselves  be  made 
the  object  of  thought,  such  cognitions  constitute  what  is  called 
Necessary  Matter,  or  as  thought,  Necessary  Truth.  All 
other  cognitions  constitute  what  is  called  Contingent  Matter 


42  PURE  LOGIC. 

or  Contingent  Truth.  As  these  latter  cognitions  approach 
more  or  less  nearly  to  the  character  of  necessary  matter, 
they  receive  in  loose  unscientific  discourse  the  denominations 
properly  belonging  to  thought  alone.  We  may,  indeed, 
classify  cognitions  in  respect  to  this  approximation  to  Neces- 
sary Truth.  In  the  first  and  highest  class,  we  should  have, 
thus,  the  pure  products  of  thought,  embracing  all  the  rela- 
tions in  the  Same  and  Different,  the  More  and  the  Less,  the 
Whole  and  the  Part,  the  Part  and  the  Complementary  Parts,  so 
far  as  these  relations  are  kept  pure  from  matter  external  to 
thought.  Here,  accordingly,  lie  all  the  truths  of  Pure  Logic 
in  the  relations  of  Judgments  to  one  another  ;  of  Concepts, 
also,  whether  of  genus  to  species,  or  of  attribute  to  involved 
attribute  ;  and,  moreover,  of  Reasonings.  For  a  single  exem- 
plification in  this  department  of  Necessary  Truth,  that  an 
attribute,  which  is  the  constituent  of  another  more  comprehen~ 
sive  attribute  belonging  to  a  class,  belongs  to  each  individual 
of  the  class,  is  a  Necessary  Truth.  Here  lie,  too,  all  the 
Truths  of  Pure  Mathematics  —  of  Magnitude  in  Geometrical 
Science,  and  of  Number  in  Arithmetic  and  Algebra,  and  in 
Higher  Quantitative  Analysis.  All  these  are  necessary 
Truths,  inasmuch  as  they  are  absolute  in  thought,  whether 
there  be  any  extended  being  to  be  measured,  any  real  objects 
to  be  numbered,  or  not ;  whatever  may  be  believed  in  respect 
to  the  nature  of  Space  and  Time,  whether  they  are  realities 
or  mere  conditions  or  forms  of  the  Intelligence.  Here  lie, 
moreover,  manifold  truths  which  are  applicable  to  objects 
only  so  far  as  they  are  proper  Being  —  the  relations  of 
Substance  and  Quality,  of  Cause  and  Effect.  These  a'e 
necessary  truths  for  thought,  whether  external  Being  be  a 
reality  or  only  an  idea. 

In  the  class  of  Contingent  Matter,  but  more  nearly  ap- 
proximating the  character  of  Necessary  Truth,  are  the  truths 
involved  in  the  relations  between  the  cognitions  given  in  Per- 
ception and  Self-Consciousness  and  those  given  in  Intuition. 
That,  for  instance,  the  body  which  is  cognized  by  perception 


JUDGMENTS.  43 

through  the  senses  exists,  is  real,  and  that  the  mind  which 
perceives  it  also  exists,  is  real,  are  truths  which  we  loosely 
call  necessary  truths.  They  are,  obviously,  not  strictly  so, 
for  the  contradictories  of  these  propositions  are  not  absurdi- 
ties. 

In  the  same  class,  but  further  removed  from  the  class  of 
necessary  truths,  are  those  expressing  relations  between  any 
two  cognitions  of  Perception.  Thus,  that  the  sun  is  bright, 
is  a  contingent  truth  of  a  lower  class  in  the  respect  of  modal- 
ity than  the  truth  that  the  sun  exists. 

We  have,  thus,  the  manifold  gradations  of  modality,  rang- 
ing from  the  faintest  possibility  up  through  all  the  degrees  of 
probability  and  of  certainty  to  the  truths  of  thought,  where 
only  we  find  that  which  is  apodictic  or  absolutely  necessary. 

Some  logicians,  including  Sir  William  Hamilton,  have  ex- 
cluded from  the  science  this  division  of  Judgments,  in  respect 
of  their  modality,  as  well  as  the  principle  upon  which  it  is 
founded,  as  not  of  proper  logical  consideration.  Sir  William 
Hamilton  adduces  two  arguments  for  this  exclusion.  One  is 
from  Example.  He  takes  the  proposition,  "Alexander  con- 
quered Darius  honorably,"  and  asserts  that  it  may  be  resolved 
into  the  proposition,  "Alexander  was  the  honorable  conqueror 
of  Darius."  By  separating  thus  the  word  containing  the 
copula  into  its  two  parts,  the  copula  part  was,  and  the  predi- 
cate part  conqueror,  and  thus  showing  that  the  modal  word, 
honorably,  really  belonged  to  the  predicate,  he  fancied  he 
showed  a  universal  fact  in  regard  to  all  forms  of  expressing 
modality,  that  they  belong  properly  to  the  predicate,  not  to 
the  copula  —  to  the  matter,  consequently,  not  to  the  form 
of  the  thought.  But  honorably  is  never  a  copula  modal ; 
and  therefore  his  whole  argument  is  fallacious.  His  other 
argument  is,  that  in  order  to  determine  the  modality  of  a 
Judgment,  we  must  go  to  the  matter,  for  so  those  logicians 
who  have  admitted  modality  as  of  proper  logical  considera- 
tion have  taught.  This  argument  is  valid  only  against  those 
who  have  taught  thus  erroneously. 

But  the  modality  regarded  by  logicians  attaches  to  the 


44  PURE  LOGIC. 

copula,  not  to  the  predicate  ;  to  the  form  of  the  thought,  con- 
sequently, not  to  the  matter.  And  the  reasoning  by  which  it 
is  excluded  would  equally  exclude  the  distinction  between 
Affirmative  and  Negative  Judgments ;  for  it  is  just  as  easy 
and  just  as  legitimate  to  remove  the  negative  from  the  copula 
to  the  predicate,  as  to  remove  thus  the  proper  copula  modal, 
as,  indeed,  is  freely  allowed  even  by  those  who  exclude  mo- 
dality, as  they  expressly  but  most  erroneously  teach  that  the 
proposition  A  is  not  B,  is  exactly  equivalent  to  A  is  non-B. 
But  proper  logical  modality,  as  we  have  seen,  like  proper 
logical  quality,  lies  in  the  thought  itself,  not  in  the  matter. 
We  may  say,  indeed,  Alexander  possibly  conquered  Darius, 
or  Alexander  was  a  possible  conqueror  of  Darius,  and  mean 
nearly  the  same  thing.  Still,  possible  conqueror  and  non-B 
are  data  presented  to  thought,  while  possibly  was,  like  is  not, 
is  of  the  essence  of  the  thought  itself.  One  form  of  expres- 
sion may,  under  some  restrictions,  be  derived  from  the  other  ; 
but  to  confound  them  is  to  confound  form  with  matter,  thought 
itself  with  the  mere  datum  to  thought. 

Thirdly,  a  Judgment  may  vary  according  to  the  degree  of 
(3  )  its  De-  identity  recognized  between  the  terras.  As  this 
gree.  identification  is  total  or  partial,  the  distinction  gives 

the  two  species  of —  1.  Judgments  of  Total  Identity ;  and,  2. 
Those  of  Partial  Identity,  with  their  subdivisions. 

This  distinction,  although  at  first  view  it  might  seem  to 
lie  rather  in  the  Terms,  may  yet  be  not  improperly  recog- 
nized as  a  subjective  element,  lying  in  the  thought  itself. 
For,  unlike  the  distinctions  that  are  founded  in  the  matter 
of  the  thought,  this  is  created  in  the  Thought-process  itself 
—  in  the  very  act  of  judging.  In  the  case  of  the  others,  the 
objects  or  terms  are  presented  to  the  Judgment  already  dis- 
tinguished, either  as  objects  or  as  truths,  as  Comprehensive 
or  Extensive  Wholes,  as  Integrate,  Substantial,  or  Causal. 
But  here  the  Judgment  itself  originates  the  distinction.  The 
two  objects  are  given  it  simply  as  wholes.  Thought  itself 
then  recognizes  them  in  relation  to  their  respective  parts, 
and  identifies   some  part  of  one   thus   recognized  with   the 


JUDGMENTS.  45 

whole  or  some  part  of  the  other.  There  is,  it  is  true,  a 
seeming  impropriety  in  founding  this  distinction  on  the  copula. 
But  it  is  only  seeming ;  for  it  should  be  borne  in  mind  that  by 
the  copula  is  properly  meant  the  entire  product  of  the  judg- 
ing activity  in  accepting  and  identifying  the  data.  Whether 
the  Judgment  shall  identify,  for  instance,  a  given  object  with 
more  or  less  of  its  parts,  is  determined,  not  by  the  datum,  but 
by  the  thought  itself. 

Looking  next  to  the  objective  element  in  a  Judgment,  the 
matter  or  the  Terms,  we  find  given  in  it  also  a  2  In  respect 
threefold  distinction.  First,  the  matter  as  thought,  of  the  Terms. 
—  and  it  is  not  matter  in  itself,  but  only  as  it  is  (1 }  Thcir 
thought,  that  can  be  here  regarded,— may  be  either  Form- 
itself  a  Judgment  or  a  simple  object  of  thought.  In  the  latter 
case  emerges  the  proper  Categorical ;  in  the  former,  the  so- 
called  Hypothetical,  Judgment. 

Secondly,  the  matter  may  be  thought  as  in  the  one  or  the 
other  of  the  two  kinds  of  Logical  Quantity,  giving  %jjff* 
rise  to  the  distinction  of  Extensive  and  Compre-   Quantity. 
hensive  Judgments,  according  as  the  terms  are  thought  in  Ex- 
tensive or  Comprehensive  Quantity. 

Thirdly,  the  matter  may  be  thought  in  either  of  the  kinds 
of  Whole,  in  which  Being  is  thought,  giving  rise  ^Their 
to  the  distinction  of  the  three  kinds  of  Judgments   Quantity. 
—  the  Integrate,  the  Substantial,  and  the  Causal.    This  prin- 
ciple of  distinction  may  be  denominated  that  of  Material  or 
Metaphysical  Quantity. 

It  might  at  first  be  supposed  that,  in  making  or  accepting 
these  distinctions,  Logic  was  transcending  its  sphere  as  a 
purely  Formal  Science,  and  corrupting  its  own  purity  by  ad- 
mitting what  concerns  properly  the  matter  of  thought.  But 
it  should  be  borne  in  mind  that  if  we  think  at  all  we  must 
think  something  —  Thought  must  have  an  object  out  of 
itself  that  is  given,  presented  to  it ;  and  it  must  think  that 
object  as  it  is,  not  as  it  is  not.  It  must,  therefore,  accept  the 
matter  as  it  is  given.  It,  however,  thinks  what  is  given  it 
only  in  its  own  proper  relations  —  those  of  Identity  and  of 

\ 


46  PURE  LOGIC. 

Whole  and  Part.  It  is  of  interest  to  Logic,  accordingly,  to 
regard  the  peculiarities  of  the  objects  given  to  Thought  only 
so  far  as  they  affect  the  relations  of  Identity,  or  of  Whole 
and  Part.  If  these  peculiarities  affect  the  nature  of  the 
Whole,  Logic  must  of  necessity  regard  them,  or  its  processes 
of  thought  become  at  once  invalidated.  The  purely  Formal 
Science  of  Mathematics  presents  a  perfect  analogy  in  its 
treatment  of  the  wholes  or  magnitudes  in  space.  It  distin- 
guishes a  Linear  Whole  from  a  Superficial  Whole,  and  both 
from  a  Solid.  Were  it  to  confound  these,  its  procedures 
would  be  invalid  and  worthless.  So  it  must  accept  the  dis- 
tinctions between  a  Right  Line  and  a  Curve;  between  Rec- 
tilinear Surfaces  and  Curved  Surfaces.  It  must  do  this  be- 
cause the  relations  of  Whole  and  Part  in  these  several  cases 
are  different.  The  sum  of  the  angles  in  a  Rectilinear  Tri- 
angle does  not  correspond  with  the  sum  of  the  angles  in  a 
Spherical  Triangle.  Any  Formal  Science  must,  therefore, 
be  able  to  distinguish  such  peculiarities  in  its  matter  as  affect 
the  purity  and  validity  of  its  formal  processes.  In  other 
words,  Logic,  although,  or  perhaps  more  accurately,  because, 
a  Formal  Science,  must  evolve  its  principles  in  such  a  way 
as  to  meet  the  peculiarities  of  the  matter  to  which  it  is  to 
apply  its  formal  procedures. 

At  the  same  time,  Logic  does  not  scrutinize  the  reality  of 
the  matter  given  it  to  be  thought,  except,  at  least,  to  see  that 
it  does  or  does  not  correspond  with  its  own  principles,  as 
whatever  contradicts  those  it  is  bound  to  reject.  It  does  not 
affect  its  Laws  or  the  integrity  and  validity  of  its  processes 
whether  there  be,  in  point  of  fact,  any  such  distinctions  in 
the  matter  as  are  given  to  it ;  as  Mathematics  does  not  in- 
quire whether  there  be  in  nature  Lines,  Surfaces,  Solids,  its 
procedures  being  just  as  legitimate  and  sure,  if  there  were 
nothing  in  reality  in  the  outer  world  to  correspond  to  these 
distinctions.  It  is  sufficient  to  vindicate  the  propriety  and 
the  necessity  of  regarding  these  cogitable  distinctions  in  mat- 
ter, simply  to  consider  that  these  distinctions  are,  in  fact, 
cogitable  —  that  they  are  possible  to  thought. 


JUDGMENTS. 


47 


The  limits  to  be  placed  in  regard  to  the  extent  to  which 
these  distinctions  should  be  admitted  are  to  be  determined  by 
the  proposed  objects  and  uses  of  the  Science.  A  system  of 
general  Logic  should  admit  only  the  most  general  distinc- 
tions. It  should  not  certainly  stop  short  of  those  which  are 
found  in  the  two  forms  in  which  Being  is  known  to  us  — 
Substance  and  Cause. 


Judgments 
are  divided, 


These  six  Divisions  of  Judgments,  it  should  be  observed, 
are,  in  reference  to  one  another,  Cross  Divisions  or  Con- 
divisions,  and  intersect  one  another.  The  same  Proposition, 
thus,  may  be  Affirmative,  Assertory,  Partial,  Categorical, 
Comprehensive,  and  Substantial. 

With  these  general  views,  in  regard  to  the  grounds  of  the 
distinctions  to  be  recognized  in  Logical  Judgments,  we  pro- 
ceed to  a  particular  consideration  of  them  in  order,  present- 
ing first  the  following  tabular  view  :  — 

1.  As  to  its  Quality,  into  (1.) 
Simple  Affirmative  and 
Negative ;  (2.)  Disjunc- 
tive. 

As  to  its  Modality,  into 
(1.)  Assertory  ;  (2.)  Prob- 
lematic ;  (3.)  Apodictic. 

3.  As  to  its  Degree,  into  (1.) 
Identical ;  (2.)  Partial. 

1.  As  to  their  Form,  into 
(1.)  Categorical ;  (2.)  Hy- 
pothetical. 

2.  As  to  their  Logical  Quan- 
tity, into  (1.)  Comprehen- 
sive ;  (2.)   Intensive. 

3.  As  to  their  Material  Quan- 
tity, into  (1.)  Integrate; 
(2.)  Substantial ;  (3.)  Cau- 
sal. 


In  respect  of  J  2 
I.  The  Copula, 


.  H.  The  Terms.  { 


48  PURE  LOGIC. 

§  25.  The  First  General  Division  of  Judgments  is 
1.  First  Di-     f°uncl'ed  on  the  Quality  of  the  Copula,  and  gives 

J^dments  aS  *tS  results  tne  two  kmds  of —  *•  Simple  Affirm. 
—as  to  ative  and  Negative  ;  and,  2.  Disjunctive  Judg- 
ments. 

An  Affirmative  Judgment  is  a  product  of  positive 
(1.)  Affirma-  thought  recognizing  sameness  between  the  Terms ; 
tiTe-  as  A  is  B ;  Virtue  is  Manliness  ;   The  Skies  are 

Blue. 

The  copula  in  the  simple  Affirmative  Proposition  is  ex- 
pressed in  Mathematical  Science  by  the  symbol  of  Equality 
or  Identity  (=)  as  a=b.  In  common  discourse,  the  inflec- 
tions of  the  verb  to  be  are  used  to  express  the  simple  copula. 

A  Negative  Judgment  is  a  product  of  negative  thought 
(2.)  Nega-  recognizing  difference  between  the  Terms ;  as  A 
tive-  is  not  B ;    Virtue  is  not  Necessity ;  The  Skies  are 

not  Cloudy. 

A  Disjunctive  Judgment  is  a  necessitated  product  of 
(3.)  Disjunc-  thought,  identifying  an  object  with  another,  or 
tive.  with  its  different,  as  A  either  is  or  is  not  B ;  vir- 

tue is  either  voluntary  or  involuntary  ;  the  skies  are  either 
light  or  dark;  the  flower  is  either  blue  or  purple. 

The  copula  is  expressed  with  the  aid  of  the  disjunctive 
particles,  as  is  either  —  or.  The  first  of  this  pair  of  particles 
is  often  omitted,  and  then  the  expression  is  equivocal,  for  the 
or  may  indicate  an  alternative  in  the  words  only  and  none  in 
the  thought,  as  in  the  proposition,  the  electricity  was  vitreous 
or  positive. 

There  are  three  distinct  forms  of  this  species  of  Judgment, 
Logical  op-  founded  on  the  diverse  kind  of  difference,  or,  as 
position.  logicians  designate  it,  of  Opposition,  that  may  be 
thought  in  the  Judgment.  First,  the  primitive  form  is  where 
the  opposition  or  difference  lies  in  the  copula  itself;  as  A  is 
B  or  is  not  B ;  virtue  either  is  voluntary  or  is  not  voluntary. 
This  must  be  regarded  as  a  single  judgment,  not  a  compound, 
for  it  is  a  single  act  of  thought,  although  embracing  more 


JUDGMENTS.  49 

than  one  element  or  factor.  In  this  case  we  have  what  is 
called  Pure  Contradictory  Opposition.  The  Law  of  Exclu- 
sion forbids  any  negative  Judgment  of  this  form. 

But  an  immediate  derivative  from  this  is  effected  by  the 
transfer  of  the  negation  or  sign  of  difference  to  the  predi- 
cate—  a  transfer  which  although  not  always,  yet  is  often 
legitimate  in  thought,  as  will  be  shown  hereafter.  So  that 
from  this  primitive  Judgment  we  obtain  the  form,  A  is  B  or 
not~B ;  Virtue  is  voluntary  or  involuntary.  In  this  form, 
while  the  opposition  is  no  longer  in  the  copula,  but  in  the 
predicate,  the  opposition  is  between  only  two  parts  or  mem- 
bers of  the  predicate,  and  is  of  such  a  nature  that  one  by  the 
necessities  of  thought  excludes  the  other.  This  is  called 
Contradictory  Opposition  ;  but,  evidently,  it  is  not  necessa- 
rily pure,  or  of  the  thought  merely  ;  it  is  only  accepted  or 
assumed  as  contradictory.  To  assure  perfect  thought,  it  will 
be  necessary  often  to  reduce  the  Judgment  to  pure  contra- 
dictory opposition.  The  fallacy  arising  from  accepting  oppo- 
sition in  the  terms  for  opposition  in  the  copula,  is  a  very 
common  one. 

From  this  second  form  of  a  Disjunctive  Judgment,  there 
springs  a  third,  in  which  the  opposition  between  the  parts 
of  the  predicate  is  not  of  such  directly  contradictory  character, 
as  that  the  one  of  necessity  excludes  the  other,  as  in  the  prop- 
osition :  The  flower  is  either  blue  or  purple.  If  the  flower  be 
not  blue,  it  does  not  necessarily  follow  that  it  is  purple;  it 
may  be  of  some  other  color,  although  it  cannot  be,  at  the  same 
time  at  least  and  in  the  same  part,  both  blue  and  purple. 
This  kind  of  opposition  in  the  terms  of  a  Judgment  is  called 
Contrary  Opposition.  "We  have  thus  the  following  distinc- 
tions :  — 

§26.  Disjunction  in  Thought  maybe  either  in  Its  kin(ls: 
the  Copula  or  in  the  Terms.  If  it  be  in  the  Cop-  victory1-1 2" 
ula,  we  have  Pure  Contradictory  Opposition.  Contrary. 

If  it  be  in  the  Terms,  it  is  either  of  Contradictory  or  of 
Contrary  Opposition. 


50  PURE  LOGIC. 

The  Opposition  is  Contradictory  when  it  lies  be* 
tvveen  two  objects  of  thought,  one  of  which  necessarily,  that 
is,  in  strict  thought,  excludes  the  other. 

It  is  Contrary  when  it  lies  between  two  or  more  objects, 
so  that  the  denial  of  one  does  not  directly  and  necessarily 
imply  the  admission  of  the  other,  or  the  reverse. 

It  will  have  been  observed  that  these  several  forms  of  Dis- 
junction really  work  so  many  gradations  in  the  logical  rigor 
of  the  Thought.  Only  the  first,  which  indeed  the  Definition 
properly  respects,  is  a  disjunction  of  strict  logical  necessity. 
The  form  A  is  B  or  is  not  B,  holds  necessarily  true  univer- 
sally, as  no  two  objects  can  be  brought  before  the  mind  in  re- 
gard to  which  Thought  is  not  necessitated  to  affirm  that  they 
are  either  the  same  or  are  not  the  same.  But  the  second 
form  or  gradation  does  not  hold  universally ;  for  we  cannot 
say  Sweetness  is  voluntary  or  involuntary,  since  it  is  neither. 
Only  when  this  form  can  be  reduced  to  the  first  is  it  of 
necessary  cogency.  The  third  form  or  gradation  is  still 
further  removed  from  the  character  of  a  necessary  logical 
form.  To  insure  for  it  this  character,  it  must  be  reduced 
through  the  second  to  the  first. 

It  is  remarkable  that  logicians,  who  have  been  most  rigid 
in  insisting  that  Logic  must  be  held  to  the  pure  form  of 
Thought  to  the  utter  exclusion  of  all  consideration  of  the 
matter  of  Thought,  have  admitted  the  second  of  these  forms 
of  Disjunction  without  a  question,  and  have  overlooked  en- 
tirely the  first,  which  is  the  only  one  that  lies  in  the  pure 
form  of  the  Thought. 

The  examples  given  express  a  disjunction  only  in  the  pred- 
icate of  the  Judgment.  But  it  may  lie  equally  well  in  the 
subject ;  thus,  either  A  or  B  is  C,  is  just  as  legitimate  a 
Judgment  as  C  is  A  or  B.  So  the  negative  form  is  equally 
competent.  Examples  in  concrete  matter  are :  either  John  or 
James  is  guilty  ;  neither  James  nor  John  is  guilty.  This  neg- 
ative form  corresponds  with  what  has  been  called  the  Re- 
motive  Judgment,  which  is  classed  as  a  species  of  Composite 


JUDGMENTS.  51 

Categorical  Judgments.1  A  Judgment,  also,  Disjunctive  in 
form,  may  be  sometimes  equivalent  to  what  has  been  termed 
the  Divisive  Judgment,  which  has  been  classed  as  a  species 
of  Categorical  Judgments  ; 1  as,  Triangles  are  either  Equilat- 
eral, Isosceles,  or  Scalene,  which  is  equivalent  to  Triangles  are 
partly  Equilateral,  partly  Isosceles,  partly  Scalene. 

§  27.  The    Second    General    Division    of    Judgments   is 
founded  on  the  Modality  of  the  copula  or  deter-      Second  Di- 
mming  act  in  the  Judgment.     This   distinction   judgments 
gives  the  three  specie3  of —  ModLuty^ 

1.  The  Assertory. 

2.  The  Problematic. 

3.  The  Apodictic,  or  Necessary. 

An  Assertory  Judgment  simply  affirms  or  (1 )  as  rt- 
denies :  as,  A  is  B ;  A  is  not  B  ;  A  is  either  B  or  G.  oiy- 

A  Problematic  Judgment  affirms  or  denies  under  the 
modification  of  Contingency:  as  A  may  be  B ;  A  (2.)  prob- 
may  be  either  B  or  0.  lematic. 

An  Apodictic  or   Necessary  Judgment   affirms   or 
denies  under  the  modification  of  Necessity :  as,  A  ^.)  Apodio- 
must  be  B ;  A  must  be  either  B  or  C ;  A  is  neces-  tlc' 
sarily  B. 

The  Modality  of  a  Judgment  may  be  expressed  by  modals, 
or,  as  they  are  sometimes  called,  modal  adverbs,  as  well  as  by 
the  mood  inflections  of  the  verb  to  be.  Thus  probably,  pos- 
sibly, contingently,  perhaps,  by  chance,  it  may  be,  and  the  like 
adverbial  expressions,  are  Copula  Modals  appropriate  to  the 
Problematic  Judgment.  The  characteristic  of  this  Judgment 
is  that  in  it  the  ground  of  the  identification  of  the  terms  is 
accepted  or  assumed  as  in  the  matter,  and  not  contained  in 
the  Thought  itself.  As  in  the  second  and  third  forms  of 
the  Disjunctive  Judgment,  so  here,  the  problematic  in  the 
matter  may  be  taken  or  assumed  as  partaking  of  the  char- 
acter of  necessity,  which  properly  comes  from  the  Thought 
alone.  This  assumption  is  not,  however,  of  strict  right,  but, 
so  to  speak,  only  by  courtesy. 

1  Drobisch,  Logik.    §§  44,  45.    Leipzig,  1851. 


52  PURE  LOGIC. 

The   modals  which   are   appropriate   to  Apodictic   Judg- 
ments are  such  as  necessarily,  unavoidably,  of  or  by  necessity. 
_,  .,  „  .  §  28.  The    Third    General    Division    of  Judg- 

Third  Dins-  °  _  ° 

ion  of  Judg-    ments  is  founded  on  the  Decree  of  Identity  predi- 

ments,  as   to  _  . 

their  Degree   cated.     This   Identity  may  be  Total  or  Partial, 

of  Identity.  ...,.„ 

giving  rise  to  the  two  species  or  — 

1.  Judgments  of  Total  Identity. 

2.  Judgments  of  Partial  Identity. 

These  varieties  of  Judgments  have  been  termed  Substitu- 
live  and  Attributive  —  a  denomination  not  pointing  to  the 
essential  ground  of  the  distinction.  It  is  true  that  in  those 
of  the  first  species  in  which  a  total  identity  is  affirmed  be- 
tween the  subject  and  the  predicate,  the  terms  are  converti- 
ble—  may  be  substituted  one  for  the  other.  But  precisely 
so  in  every  Judgment,  so  much  of  either  term  as  is  taken  is 
exactly  convertible  with  whatever  part  of  the  other  is  taken 
in  the  Judgment ;  and  so  far  as  the  validity  of  the  Judgment 
is  concerned,  it  is  a  matter  of  entire  indifference  which  is 
made  the  subject  or  which  the  predicate.  It  is  the  occasion 
of  the  use  which  ever  determines  this.  And  in  regard  to 
the  name  given  to  the  other  species,  Attributive,  all  Judg- 
ments are  attributive,  since  it  is  of  their  very  essence  that 
they  attribute. 

The  first  of  these  two  species  of  Judgments  regarded  as 
expressed,  that  is,  as  Propositions,  embraces  two  varieties. 
1.  The  Tautological,  in  which  the  terms  are  expressed  in  the 
same  verbal  form,  as,  A  is  A.  2.  Proper  Identical,  in  which 
the  Terms  are  expressed  in  different  forms  of  words,  as,  Virtue 
is  manliness  ;  likewise  in  Algebraic  Formulas,  as,  a  =  b  -J-  c  ; 
and  in  Exact  Definitions,  as,  Virtue  is  right  action. 

Those  of  the  other  species  make  up  the  great  body  of  prop- 
ositions occurring  in  discourse.  In  them  one  of  the  terms 
is  always  affirmed  to  be  related  to  the  other  as  Part  to  a 
Whole.  Thus  in  the  Proposition  Alan  is  two-footed,  the  char- 
acter two-footed  is  affirmed  to  be  one  of  the  characters  that 
make  up  the  whole  notion,  man.     In  the  Proposition  Man  is 


JUDGMENTS.  53 

a  biped,  man  is  affirmed  to  be  a  part  of  the  class  of  objects 
called  bipeds  ;  or,  what  is  an  exactly  equivalent  explication 
in  the  former  proposition,  one  of  the  parts  of  the  whole 
notion,  man,  is  identified  with  the  character  two-footed ;  in 
the  latter,  the  part  or  species,  man,  is  identified  with  one  of 
the  parts  that  make  up  the  whole  genus,  biped. 

It  will  be  convenient,  and  will  involve  no  serious  liability 
to  error,  if  we  adopt  the  familiar  designations  of  Identical 
Judgments  and  Partial  Judgments  for  the  two  species  of  this 
class.     "We  then  have  the  following  definitions. 

An  Identical  Judgment  is  one  in  which  the  subject  is 
identified  wholly  with  the  predicate ;    as,  a  =  b;  (1  ,  Identi. 
Virtue  is  manliness  ;  Man  is  rational  animal.         cal- 

A  Partial  Judgment  is  one  in  which  the  subject  is  but 
partially  identified  with  the  Predicate,  in  which 

i     •  .  m  (2-)  Partial. 

case  the  relation  recognized  between  the  Terms  is 

that  of  Whole  and  Part;  as,  Man  is  rational;  Man  is  a 

biped. 

A  Tautological   Proposition   is  one  in  which  the 
Terms  are  expressed  in  the  same  verbal  form  ;  as  (3  ,  Taut0. 
a  is  a  ;   Gold  is  gold.  logical. 

§  29.   The    Fourth    General   Division  of  Judgments    is 
founded  on  the  diverse  character  of  the  Terms.   Fourth  Di- 
These  we  have  found  to  be  of  three  classes.     1.  Judgments 
Individual  or  Simple  Objects.    2.  Concepts.    And,  pj^J^®  of 
3.  Judgments.     Those  Judgments  which  have  for  thek  Terms. 
their  Terms  other  Judgments,  possess  some  peculiar  charac- 
ters which  make  it  desirable  to  keep  them  distinct  from  the 
others.     They  have  been  in  fact  familiarly  distinguished  by 
the   denomination    of  Hypothetical,  while  other  Judgments 
have  been  called  simply  Categorical.     We  have  thus  the  fol- 
lowing definitions. 

A  Categorical  Judgment  is  one  the  Terms  of  which 
are  Individual  or  Simple  Objects  or  Concepts ;  as,   «  .  Categor. 
Bucephalus  is   a   quadruped;  Man  is   rational;   ical- 
Fire  burns. 


54  PURE  LOGIC. 

A  Hypothetical  Judgment  is  one  the  Terms  of  which 
(2  )  Hypo-  are  Judgments  ;  as,  If  A  is  B,  O  is  D  ;  If  virtue 
theticai.  {s  voluntary,  vice  is  voluntary  ;  That  A  is  B  im- 
plies that  G  is  D. 

This  last  species  of  Judgments  has  received  its  name  from 
the  verbal  form  in  which  they  more  commonly  appear.  They 
are  ordinarily  expressed  under  the  form  of  an  hypothesis  or 
condition  indicated  by  the  conjunction  if  It  must  not  be 
supposed  that  this  suppositive  or  conditional  character  reaches 
beyond  the  Terms  of  the  Judgment,  or  affects  at  all  the  ab- 
solute nature  of  the  Judgment  itself.  The  relation  of  iden- 
tity between  the  Terms  is  just  as  absolute  as  in  any  Judg- 
ment. But  the  assumed  character  of  the  datum,  or  matter, 
is  here,  through  the  imperfections  of  language,  signalized  by 
the  conjunction  prefixed  to  the  term  ;  as  where  a  judgment 
is  used  as  an  object  of  thought,  we  ordinarily  mark  it  as  thus 
used  by  a  grammatical  conjunction,  such  as  if  and  that. 

It  is  to  be  noticed  here  that,  as  elsewhere  more  fully  ex- 
hibited, there  are  two  fundamental  relationships  in  Thought 
as  essentially  regulated  by  Quantity  ;  the  one  between  the 
Whole  and  Part,  the  other  between  a  Part  and  its  Comple- 
mentary Part.  The  first  is  the  only  relationship  in  which 
logicians  have  exhibited  Thought;  and  all  their  teachings 
and  their  illustrations  have  been  confined  to  that.  Perhaps, 
for  the  sake  of  simplicity,  it  may  be  expedient  to  limit  the 
illustrations,  generally  and  introductorily,  to  a  single  and  a 
more  familiar  relationship.  But  it  would  involve  serious 
error  if  that  should  be  throughout  exhibited  as  the  only  rela- 
tionship in  Thought.  And  here,  precisely,  in  their  treatment 
of  Hypothetical  Judgments,  logicians  have  experienced  the 
evil  consequences  of  partial  and  one-sided  views,  as  their  ex- 
positions of  this  product  of  Thought  are  discordant  and  con- 
fused. It  should  be  distinctly  noticed  then,  that  under  the 
common  form  of  the  Hypothetical  Judgment,  either  of  the 
two  relationships  of  Quantity,  of  Whole  to  Part,  or  of  Part 
to  Complementary  Part,  may  be  indicated.     Thus  in  the 


JUDGMENTS.  55 

Judgment,  If  virtue  is  free,  temperance  is  free,  the  relation- 
ship is  that  of  Whole  to  Part ;  while  in  the  Judgment,  If 
virtue  is  free,  vice  is  free,  it  is  that  of  Part  and  Complement- 
ary Part,  virtue  and  vice  being  complementary  parts  of  the 
whole  — free  action. 

In  either  case  the  antecedent  clause  is  said,  indifferently,  to 
determine,  to  condition,  to  imply,  or  to  involve  the  consequent 
clause,  or  the  reverse.  For  it  is  to  be  remarked,  that  the 
consequent  or  predicate  clause  may  condition  as  well  as  be 
conditioned  by  the  other.  This  is,  however,  not  to  be  taken 
unqualifiedly  and  without  explanation.  For  while  in  the  case 
in  which  the  movement  of  Thought  is  between  Complement- 
ary Parts,  the  two  clauses  may,  of  course,  —  except  as  one  is 
assumed  as  a  positive,  and  the  other  as  a  negative,  —  stand  in 
perfectly  reciprocal  relations  ;  in  the  other  case,  the  whole 
conditions  the  part  otherwise  than  as  the  Part  the  Whole. 
Thus  vice,  as  complementary  part,  conditions  virtue  as  much 
and  in  the  same  way  as  virtue  conditions  vice  ;  but  temper- 
ance conditions  virtue  as  containing  it  as  one  of  its  constitu- 
ent characters,  while  virtue  conditions  temperance  as  being 
contained  in  it. 

A  hypothetical  Judgment  has  both  its  Terms  Judgments. 
If  but  one  Term  be  a  Judgment,  as  may  be  the  case,  the 
Judgment  is  classed  as  Categorical. 

§  30.  The  characteristics  of  the  Hypothetical  and  the 
Disjunctive  Judgment  may  both  concur  in  the  same  Hypothetico- 
Judgment;  we  then  have  the  Hypothetico- Disjunct-  Disjunctive. 
ive,  or,  as  it  has  been  called,  the  Dilemma  ;  as,  If  A  is  B  it 
is  either  C  or  non-  C ;  If  an  action  be  prohibited,  it  is  pro- 
hibited by  natural  or  by  positive  law.  The  explication  of 
this  Judgment  is  easy.  The  former  of  these  examples 
means  :  The  truth  that  A  is  B  contains  or  involves  the  truth 
that  A  is  either  C  or  non-  C.  The  latter  means  :  The  truth 
that  an  action  is  prohibited  involves  the  truth  that  it  is  pro- 
hibited by  natural  or  by  positive  laws.  We  thus  have  the 
definition  :  — 


56  PURE  LOGIC. 

A  Hypothetico-Disjunctive  Judgment  is  a  Disjunct- 
ive Judgment  with  truths  or  judgments  instead  of  simple 
objects  for  its  Terms. 

It  may  be  remarked  here  that  Judgments  of  different 
classes  may  be  combined  almost  indefinitely  ;  but  this  par- 
ticular combination  of  the  Disjunctive  with  the  Hypothetical 
has  attained  a  classical  distinction  from  its  use  by  old  Gre- 
cian sophists. 

§  31.  The  Fifth  General  Division  of  Judgments  is 
Fifth  Divis-  founded  on  the  two  kinds  of  Logical  Quantity  — 
ionofjudg-    Extensive   and    Comprehensive   or    Intensive  — 

merits,  as  to  r 

their  Logical   which  give  the  two  species  of  Extensive  and  Com- 

Quantity.  &.  f 

prehensive  or  Intensive  Judgments. 

An  Extensive  Judgment  is  one  in  which  the  Terms  are 
(l )  Exten-  taken  in  the  Quantity  of  Extension  ;  as,  Bucepha- 
61ve-  lus  is  a  quadruped  ;  that  is,  Bucephalus  is  one  of 

the  class  quadruped. 

A  Comprehensive  or  Intensive  Judgment  is  one  in 
(2.)  Compre-  which  the  Terms  are  taken   in  the  Quantity  of 

hensive    or  .  »»•/•/•  i 

intensive.  Comprehension  ;  as,  Bucephalus  is  four-footed ; 
that  is,  Bucephalus  in  one  of  his  attributes  is  four-footed,  or 
Bucephalus  contains  the  character  four-footed. 

In  an  Extensive  Judgment,  when  affirming  only  partial 
identity,  the  predicate  is  affirmed  to  stand  in  the  relation  of 
whole  to  the  subject.  In  a  Comprehensive  Judgment,  when 
of  partial  identity,  the  subject  is  the  containing  whole,  and 
the  predicate  is  the  part  affirmed  in  the  Judgment  to  be  con- 
tained in  the  subject. 

Before  Sir  William  Hamilton,  logicians  had  generally 
viewed  all  propositions  as  being  of  Extensive  Quantity  only. 
They  accordingly  divided  them  into  four  species,  viz  :  1. 
Universal,  in  which  the  subject  is  taken  in  its  entire  sphere, 
as,  All  men  are  mortal.  2.  Particular,  as  Some  men  are 
learned.  3.  Individual  or  Singidar,  in  which  the  subject  is 
an  individual.  And,  4.  Indefinite,  in  which  the  subject  is 
not  articulately  declared  to  be  either  Universal,  Particular, 


JUDGMENTS.  57 

or  Singular.  Rejecting  this  division,  Hamilton  proposes  that 
the  subordinate  divisions  of  Judgments  in  respect  of  their 
Extensive  Quantity  be  those  of —  (1)  a  Determinate,  and  (2) 
those  of  an  Indeterminate,  Quantity;  the  former  including 
the  Universal  as  one  species,  and  the  Individual  as  the  other 
species,  and  the  latter  class  corresponding  to  the  Particular. 

The  two  kinds  of  Judgments  determined  in  respect  of  their 
*  Quantity,  as  Universal  and  Particular,  being  combined  with 
two  determined  by  their  simple  Quality,  the  Affirmative  and 
the  Negative,  in  their  diverse  combinations  give  rise  to  four 
species :  the  Universal  Affirmative,  the  Universal  Negative, 
the  Particular  Affirmative,  and  the  Particular  Negative ; 
and,  to  facilitate  the  statement  and  analysis  of  the  syllogism, 
these  four  have  by  logicians  been  designated  by  the  vowels 
A,  E,  I,  0.  The  Universal  Affirmative  are  designated  by 
A ;  the  Universal  Negative  by  E  ;  the  Particular  Affirma- 
ative  by  I ;  and  the  Particular  Negative  by  O. 

But  this  classification  originating  in  an  extremely  limited 
view  of  the  diverse  character  of  Judgments,  and  overlooking 
the  distinctions  both  of  Logical  and  of  Material  or  Meta- 
physical Quantity,  as  well  as  excluding  all  consideration  of 
Disjunctive  and  Hypothetical  Judgments,  may  well  be  dis- 
carded. It  deserves  mention  only  as  of  the  past  and  as  his- 
torical. 

§  32.  The  Sixth  General  Division  of  Judgments  is 
founded  on  the  Material  or  Metaphysical  Quantity  Sixth  Divis- 
of  the  Terms,  as  forming  Integrate,  Substantial,  or  ments  as  to 
Causal  Wholes.  This  distinction  gives  rise  to  the  whoiein  the 
three  species  of  Integrate,  Substantial,  and  Causal  erms' 
Judgments. 

An  Integrate  Judgment  is  one  in  which  the  Terms  are 
regarded  as  Integrate  Wholes  ;  as,  a-=.b-\-c;  Man   ( rateInte* 
is  Soul  and  Body. 

A  Substantial  Judgment  is  one  in  which  the  Terms 
are  viewed  in  the  relations  of  a  Substantial  Whole,   (2  )  substan- 
that  is,  of  Substance  and  Attribute;  as,  Man  is   tiaL 
rational. 


58  PURE  LOGIC. 

A  Causal  Judgment  is  one  in  which  the  Terms  are 
(3.)  Causal,     viewed  in  the  relations  of  a  Causal  Whole,  or  of 
Cause  and  Effect ;  as,  John  is  studying  ;  The  Sun 
illuminates  the  planets. 

The  Copula  in  the  Integrate  Judgment  is  variously  ex- 
pressed in  language,  as  by  is,  consists  of,  is  composed  of,  is 
constituted  of,  is  made  up  of  equals,  is  equivalent  to,  is  iden- 
tical with,  is  the  same  as,  and  the  like. 

In  the  Substantial  Judgment  it  is  expressed  by  is,  contains, 
comprehends,  includes,  involves,  implies,  and  the  like. 

In  the  Causal  Judgment  it  is  generally  and  distinctively 
expressed  by  inflections  of  verbs,  as  illuminates,  produces,  or 
by  is,  with  participial  forms,  as,  is  illuminating,  is  producing. 

The  expressions  vary  according  as  the  Whole  or  the  Part  is 
presented  as  the  Subject  in  the  Judgment.  Thus  when  the 
Whole  is  the  Subject,  the  forms  in  the  Integrate  species  are : 
Man  is  composed  of  soul  and  body;  Virtue  comprehends 
freedom  ;  Heat  expands  bodies.  When  the  Part  is  the  Sub- 
ject, the  forms  are  such  as  these :  Soul  and  Body  compose 
man  ;  Freedom  is  comprehended  in  virtue  ;  Bodies  are  ex- 
panded by  heat. 

The  relations  between  the  Whole  and  the  Parts  are  indi- 
cated by  prepositions :  in  the  Integrate  Whole  by  of,  as, 
Body  and  Soul  are  parts  of  man  ;  in  the  Substantial  and  in 
Comprehensive  Quantity,  by  in,  as,  Rational  is  contained  in 
man  ;  in  Extensive  Quantity,  by  under,  as,  African  is  con- 
tained under  man  ;  in-  the  Causal,  by  through  or  by,  as,  Bod- 
ies are  expanded  by  heat. 

§  33.  In  their  relation  to  one  another,  Judgments  are 
Distinctions     distinguished  in  various  wavs.    It  will  be  sufficient 

of  Judg-  °     .  J 

ments  in  re-   to  state  in  a  summary  manner  such  distinctions  as 

lation  to  one     .  .  "  . 

another.         nave  been  more  generally  recognized. 

The  most  important  of  these  relations  is  that  which  arises 
from  the  transposition  of  the  Terms,  so  that  the 

Conversion.       _       . 

Subject  and  the  Predicate  change  places.     This 
transposition  is  technically  called  Conversion,  and  the  prop- 


JUDGMENTS.  59 

osition  arising  from  the  conversion  is  called,  in  relation  to 
the  proposition  in  its  first  form,  the  Converse.  Thus,  Right 
free  action  is  virtue  is  the  Converse  of  Virtue  is  right  free 
action. 

"  When  the  matter  and  form  of  two  Judgments  are  con- 
sidered as  the  same,  they  are  called  Identical,  Con-  Judffmenta 
vertible,  Equal,  or  Equivalent  (propositions  iden-  identical. 
ticce,  pares,  convertibles,  ccquipollentes)  ;    on    the 
opposite  alternative,  they  are  called  Different  (pr. 
diver  see).     If  considered  in  certain   respects   the  Re]at}vejy 
same,  in  others  different,  they  are  called  Relative-  identical. 
ly  Identical,  Similar,  or  Cognate  (pr.  relative  identicce,  simi- 
les, affines,  cognates).     This  resemblance  may  be    either  in 
the  subject  and  comprehension,  or  in  the   predicate  and  ex- 
tension.     If  they   have   a   similar   subject,  their 
predicates  are  Disparate  (disparata)  ;  if  a  similar 
predicate,  their  subjects  are  Disjunct  (disjuncta).   Disjunct. 

"  When  two  judgments  differ  merely  in  their  quantity  of 
extension,  and  the  one  is,  therefore,  a  particular,  the  other 
a  general,  they  are  said  to  be  subordinated,  and  their  rela- 
tion is  called  Subordination  (subordinatio).     The   Subaiter. 
subordinating  (or  as  it  might,  perhaps,  be   more   nant- 
properly  styled,  the  superordinate)  judgment,  is  called  the 
Subalternant  (subalternans)  ;  the  subordinate  judg-   Sut)alter. 
ment  is  called  the  Subalternate  (subalternatum).       nate- 

"  When,  of  two  or  more  judgments,  the  one  affirms,  the 
other  denies,  and  when  they  are  thus  reciprocally  opposition  of 
different  in  quality,  they  are  said  to  be  Opposed  Judgments. 
or  Conflictive  (pr.  oppositce,  avTiKiLjxevai),  and  their  relation, 
in  this  respect,  is  called  Opposition  (oppositio).  This  oppo- 
sition is  either  that  of  Contradiction  or  Repugnance  (contra- 
dictio,  avTLcjxMTLs),  or  that  of  Contrariety  (contrarietas,  iiuv- 
nor>7s) . 

"If  neither  contradiction  nor  contrariety  exists,  the  judg- 
ments are  called  Congruent  (pr.  congruentes,  con-   Congruent 
sonantes,  consentientes).    In  regard  to  this  last  state-   Judgments. 


60  PURE  LOGIC. 

Subcontrarr  merjt  ^  's  stated  in  logical  books,  in  general,  that 
opposition,  there  is  an  opposition  of  what  are  called  Subcon- 
traries  (subcontrarid) ,  meaning  by  these  particular  proposi- 
tions of  different  quality,  as,  for  example,  some  A  are  B, 
some  A  are  not  B  ;  or,  some  men  are  learned,  some  men  are 
not  learned  ;  and  they  are  called  Subcontraries,  as  they  stand 
subordinated  to  the  universal  contrary  propositions  —  All  A 
are  B,  no  A  is  B  ;  or,  All  men  are  learned,  no  man  is  learned. 
But  this  is  a  mistake  ;  there  is  no  opposition  between  Sub- 
contraries  ;  for  both  may  at  once  be  maintained,  as  boih  at 
once  must  be  true  if  the  some  be  a  negation  of  all.  They 
cannot,  however,  both  be  false.  The  opposition  in  this  case 
is  only  apparent ;  and  it  was  probably  only  laid  down  from 
a  love  of  symmetry,  in  oi'der  to  make  out  the  opposition  of 
all  the  corners  in  the  square  of  Opposition,  which  may  be 
found  in  many  works  on  Logic. 

"It  may  be  proper  to  add  certain  distinctions  of  judgments 
Distinction  an<^  propositions,  which,  though  not  strictly  of  a 
of  Proposi-     logical    character,  it   is    of  importance  should  be 

tions  not  °  '  l 

strictly  logi-   known.     Considered  in  a  material  point  of  view, 

all  judgments  are,  in  the  first  place,  distinguished 

Theoretical     mj0   Theoretical  and  Practical.     Theoretical  are 

and  Practi- 

cal-  such  as  declare  that  a  certain  character  belongs  or 

does  not  belong  to  a  certain  object ;  Practical,  such  as  declare 
that  something  can  be  or  ought  to  be  done  —  brought  to  bear. 
"  Theoretical,  as  well  as  practical  judgments,  are  either 
indemon-  Indemonstrable,  when  they  are  evident  of  them- 
D^monslra-  selves  ;  when  they  do  not  require,  and  when  they 
ble-  are  incapable  of  proof:  or  they  are  Demonstrable, 

when  they  are  not  immediately  apparent  as  true  or  false,  but 
require  some  external  reason  to  establish  their  truth  or  false- 
hood. 

"  Indemonstrable  propositions  are  absolute  principles  (<xpxat'» 
principia)  ;  that  is,  from  which  in  the  construction  of  a  sys- 
tem of  science,  cognitions  altogether  certain  not  only  are,  but 
must  be,  derived.    Demonstrable  propositions,  on  the  other 


JUDGMENTS.  61 

hand,  can,  at  best,  constitute  only  relative  principles ;  that  is, 
such  as,  themselves  requiring  a  higher  principle  for  their 
warrant,  may  yet  afford  the  basis  of  sundry  other  proposi- 
tions. 

"  If  the   indemonstrable  propositions  be  of  a   theoretical 
character,  they  are  called  Axioms  ;  if  of  a  practi-   Axioms  and 
cal  character,  Postulates.     The  former  are  princi-   Postulates. 
pies  of  immediate  certainty ;  the  latter,  principles  of  imme- 
diate application. 

"  Demonstrable  propositions,  if  of  a  theoretical  nature,  are 
called    Theorems  (theoremata) :  if   of  a  practical, 

v  '  .      Theorems 

Problems  (problemata.)      The  former,  as  proposi-   and  Prob- 
tions  of  a  mediate  certainty,  require  proof;  they, 
therefore,  consist  of  a    Thesis  and  its  Demonstration ;  the 
latter,  as  of  mediate  application,  suppose  a  Question  (quces- 
tio)  and  its  Solution  (resolutio). 

"As    species  of  the   foregoing,  there  are,  likewise,  distin- 
guished   Corollaries  (consectaria,  corollaria),  that 

,  .    ,      n  .^i  /•     Corollaries. 

is,  propositions  wluch,  now,  without  a  new  proof, 
out  of  theorems  or/postulates  previously  demonstrated.    Prop- 
ositions, whose  validity  rests  on  observation  or  experiment, 
are   called    Experiential,   Experimental  Proposi-  Experiment_ 
tions      (empiremata,    experienticz,    experimenta)  ;   ^  Pr°P°si- 
Hypotheses,   that    is,    propositions   which    are    as- 

...  .....  .  ,  .    .  Hypotheses. 

suraed  with   probability,  in  order   to  explain  or 
prove  something  else  which  cannot  otherwise  be  explained  or 
proved ;   Lemmata,  that  is,  propositions  borrowed 
from  another  science,  or  from  another  part  of  the 
science,  in  order  to  serve  as  subsidiary  propositions 
in  the  science  of  which  we  treat ;    finally,  Scho- 
lia, that  is,  propositions  which  only  serve  as  illustrations  of 
what  is  considered  in  chief.     The  clearest  and  most  appro- 
priate examples  of  these  various  kinds  of  propositions  are 
given  in  mathematics." 


CHAPTER  V. 

THE    PRODUCTS    OF   THOUGHT. II.    CONCEPTS. 

§  34.  The  Second  gradation  of  Thought  is  the  Concept. 
It  is  derived  from  the  primitive  product,  the  Judgment,  by 
Fonnationof  an  act  °^  syntnesis  or  composition.  It  accordingly 
Concepts.  presupposes  two  or  more  Judgments,  and,  if  a  valid 
product  of  Thought,  can  always  be  resolved  back  into  them. 
It  can,  in  fact,  be  verified  only  by  being  thus  referred  back  to 
the  Judgments  from  which  it  is  derived.  It  is  formed  either 
by  the  synthesis  of  the  Subjects  of  two  or  more  Judgments, 
or  by  a  synthesis  of  their  Predicates  —  an  alternative  which 
gives  rise  to  the  two  fundamental  classes  of  Concepts.  It 
may  conduce  to  clearness  to  exemplify  the  process  of  forming 
the  Concept  in  these  two  ways  separately. . 

First,  then,  if  we  synthesize  the  subjects,  the  procedure 
will  be  as  follows :  The  Judgments,  out  of  which  the  Con- 
cept is  to  be  formed,  we  will  assume  to  be  —  Socrates  is  ra- 
tional;  Cicero  is  rational ;  James  is  rational.  By  uniting 
the  subjects,  we  have  Socrates  and  Cicero  and  James,  and 
marking  the  union  by  a  single  term  which  shall  embrace  them 
all  in  one,  we  will  say,  man,  we  have  the  union  signalized  in 
language.  This  union  of  the  differing  subjects  of  several 
propositions  having  a  common  predicate  is  called  a  Concept ; 
in  this  case  a  Concept  in  Extensive  Quantity.  The  formula 
for  the  formation  of  all  Concepts  of  this  class  is,  accordingly  : 
The  Judgments,  B  is  A,  C  is  A,  give  the  Concept  (B~\-C), 
or  when  signalized  in  language  by  one  term,  the  Concept  D ; 
or  in  brief:  The  Judgments  B  is  A,  C is  A,  give  B-\-C=z 
the  Concept  D. 


CONCEPTS.  63 

The  procedure  in  forming  Concepts  of  the  other  class  is 
analogous.  Here  the  Subject  remains  the  same,  and  the 
Concept  arises  from  the  synthesis  of  the  Predicates  which 
differ.  Thus,  the  Predicates  in  the  Judgments,  Socrates  is 
rational,  Socrates  is  animal,  being  united,  we  have  rational 
and  animal,  or  signalizing  the  union  by  a  single  term,  we 
have  the  Concept,  Man.  The  term  Man  here,  it  will  be  ob- 
served, means  a  complement  of  attributes,  as  rational,  ani- 
mal, not,  as  before,  of  subjects,  as  Socrates,  &c.  This  is  a 
Concept  in  Comprehensive  Quantity  ;  the  formula  of  which 
is :  The  Judgments  A  is  B,  A  is  C,  give,  by  synthesis  of  the 
differing  Predicates,  the  aggregate  (B-\-C),  which  signalized 
as  one  in  Language  is  expressed  by  D.  Or  the  Judgments 
A  is  B,  A  is  C,  give  Concept  (B-\-C)  =  D. 

§  35.  A  Concept  may  be  defined,  accordingly,  to  be  a 
product  of  Thought,  resulting  from  the  synthesis  Definitionof 
of  the  Subjects  or  of  the  Predicates  in  several  concept. 
Judgments. 

The  common  Subject  in  a  Predicate- Concept,  or  the  com- 
mon Predicate  in  a  Subject-Concept,  on  which  the  Concept 
is  formed,  is  called  its  Base. 

The  name,  Concept,  is  derived  from  the  Latin  word  Con- 
ceptum,  meaning  something  taken  with  another.  The  corre- 
sponding word  used  to  denote  the  act  of  forming  a  Concept  is 
Conception,  which  is  also  in  common  discourse  often  used  to 
denote  the  product.  It  is  used,  in  fact,  like  other  words  of 
this  kind,  in  the  threefold  import  of  faculty,  act,  and  product. 

§  36.  The  Law  of  Identity,  or  as,  in  its  fuller  expression, 
it  may  be  denominated,  the  Law  of  the  Same  and 

t-v«>  ■        mi  •  1  i  •       Conceptsun- 

JDifterent,  it  will  have  been  seen,  presides  over  this  der  Law  oi 
product  of  Thought,  as  over  the  Judgment.  No 
valid  Concept  can  be  formed,  unless  from  Judgments  which 
have  either  identical  subjects  or  identical  predicates.  The 
Concept  arises  from  the  Synthesis  of  the  different  under  the 
same  ;  of  different  subjects  having  the  same  predicate,  or  of 
different  predicates  having  the  same  subject.    In  other  words, 


64  PURE  LOGIC. 

in  the  Base  js  to  be  found  the  identifying  principle  governing 
in  the  Concept. 

§  37.  It  will  have  been  observed,  moreover,  from  the 
Concept  a      mode  of  its   formation,  as  given  in  §  34,  that  a 

Relative  Cog-  .  .  ,      . 

nition.  Concept  is  essentially  a  relative  cognition.     It  is 

not  only  the  result  of  a  synthesis,  not  only  the  aggregate  of 
a  plurality  of  Judgments,  and  accordingly  of  relative  cogni- 
tions, but  the  cognitions  that  are  brought  together  in  this 
synthesis  sustain  a  determined  and  peculiar  relation  to  one 
another.  If  the  Concepts  be  formed  from  the  subjects  of  the 
Judgments,  those  Judgments  must  have  a  common — the 
same  predicate  ;  if  from  the  predicates,  the  Judgments  must 
have  the  same  subject.  Concepts  are  thus  from  their  very 
nature  relative  cognitions,  and  the  principle  of  relation  is  in 
the  sameness  of  the  term  of  the  Judgment  which  is  not  syn- 
thesized into  the  Concept  — in  its  Base. 

Concepts,  however,  differ  from  Judgments,  as  relative  cog- 
nitions, in  this  respect :  that  in  the  Judgment  the  relation  is 
explicit,  while  in  the  Concept  it  is  only  implied.  Thus  in 
the  Judgment,  Man  is  rational  animal,  the  relation  is  ar- 
ticulately declared  ;  but  in  the  Concept,  Man,  the  relation  to 
the  other  term  of  the  Judgment  from  which  it  is  derived, 
although  real,  is  not  expressed,  but  only  implied.  The  Base 
of  the  Concept,  although  real,  is  not  expressed.  " 

§  38.  Still  further,  a  Concept  is  essentially  a  one-sided 
Concept  a       cognition.     It  is  formed  from  but  one  side  of  a 

one-sided  . 

Cognition.  Judgment,  from  the  Subject  or  from  the  Predi- 
cate. It  may  be  regarded,  indeed,  as  an  aggregate  of  Judg- 
ments, that  is,  a  synthesized  or  composite  Judgment,  with  the 
single  term  —  the  Base,  and  the  Copula  dropped. 

A  Concept,  however,  always  implies  the  Judgments  from 
which  it  is  derived  ;  it  implies  the  other  term,  which  has 
been  dropped,  but  which  is  the  indispensable  condition  of  its 
being  formed,  and  is,  therefore,  appropriately  denominated 
the  Base  of  the  Concept ;  and  also  implies  that  this  Base 
has  been  identified  with  each  of  the  terms  which  compose 
the  Concept. 


CONCEPTS.  65 

Although  a  Concept  has  this  character  of  one-sidedness,  it 
must  not  be  supposed  that  it  is  properly  an  inadequate  cog- 
nition, as  some  logicians  have  taught.  Of  all  objects  of 
thought,  that  of  a  Concept  is  most  exactly  and  adequately 
embraced  in  the  thought ;  of  all  object-cognitions,  the  cog- 
nition in  a  Concept  is  the  most  adequate.  A  Concept  is  not, 
indeed,  an  adequate  cognition  of  any  individual  embraced 
under  it,  or  of  any  simple  attribute  embraced  in  it.  But 
these  are  not  the  objects  thought  in  Concepts.  A  Concept 
is  ever  just  the  cognition  of  the  subjects  embraced  under  it 
or  the  predicates  embraced  in  it ;  it  is  of  course  a  perfectly 
adequate  cognition  of  its  proper  object. 

From  the  inadequacy  of  language  to  express  perfectly  and 
fully  the  characters  of  thought,  a  word  expressing  a  Concept 
is  for  the  most  part  at  least  used  indifferently  both  for  a  sub- 
ject-concept and  also  for  a  predicate-concept.  Man,  thus,  both 
denotes  an  aggregate  of  subjects,  as  Soci-ates,  &c,  and  also  of 
predicates  or  attributes,  as  rational,  &c.  For  accurate  and 
valid  Thought,  it  becomes  necessary  to  distinguish  these  uses  ; 
or,  out  of  the  confusion,  error  will  be  likely  to  arise.  This 
distinction  is  sometimes  marked,  when  a  Concept  is  used  as  a 
term  of  a  Judgment,  by  some  peculiarity  in  the  form  of  ex- 
pression. Thus  in  the  propositions,  Man  is  two-footed,  Man 
is  a  bi-ped,  in  the  former,  the  Concept,  Man,  is  obviously  a 
predicate-concept;  in  the  latter,  a  subject-concept.  Often 
the  distinction  emerges  only  in  the  more  advanced  progress 
of  the  thought,  as  in  a  course  of  reasoning.  It  is  natural  to 
anticipate  that  the  confusion  might,  in  continued  discourse, 
brin"  in  serious  error  which  could  not  be  corrected  nor  indeed 
be  brought  to  light  without  the  application  of  the  distinction. 
This  will,  in  the  proper  place,  be  fully  exemplified.  It  is 
sufficient  here  to  expose  the  reality  and  the  probable  impor- 
tance of  the  distinction  to  correct  and  valid  thought. 

§  39.  It  will  occur  to  the  reflecting  mind,  on  this  exposition 
of  the  mode  in  which  Concepts  are  formed,  that  Concept8  not 
they  are  mere  products  of  Thought,  aggregates  of  Re»'ltie* 


66  PURE  LOGIC. 

Subjects,  or  aggregates  of  Predicates,  and  do  not  imply  ne- 
cessarily any  exactly  corresponding  aggregates  in  the  reality 
of  things.  How  many  individual  subjects  of  Judgments  shall 
be  combined,  or  how  many  predicates,  are  questions  that  will 
be  determined  by  such  considerations  as  those  of  extent  of 
observation,  practicability  of  aggregation,  convenience  of  use, 
the  needs  of  occasion,  and  the  like.  The  extent  of  the  aggre- 
gation, therefore,  varies  indefinitely  with  the  occasions  of 
Thought ;  and  it  is  not  to  be  supposed  that  the  constitution 
of  things  around  us  fluctuates  precisely  with  the  fluctuations 
of  Thought.  As  the  mathematical  analyst,  in  the  progress  of 
his  demonstration,  finds  it  convenient  to  substitute  single 
letters  or  symbols  to  denote  a  number  of  quantities  in  some 
respect  of  like  character,  so  Thought,  for  its  own  manifold 
conveniences,  often  aggregates  like  elements  and  signalizes 
them  by  single  words.  It  does  not  thereby  change  the  con- 
stituted system  of  things. 

Concepts,  thus,  and  so  the  words  in  which  they  are  embod- 
ied and  maintain  their  existence,  are  not  fixed  and  constant 
as  inhering  in  the  stability  and  constancy  of  nature.  They 
rise  and  sink  with  the  ever-varying  vicissitudes  of  occasion. 
They  are  not,  however,  any  more  than  the  assumed  general 
symbols  in  a  mathematical  process,  illusory  and  empty.  They 
are  ever  significant ;  they  ever  suppose  and  express  what  is 
similar,  or  rather,  express  recognized  identities  in  the  objects 
of  thought.  They  can,  in  fact,  simply  by  reversing  the  proc- 
ess by  which  they  were  formed,  ever  be  traced  through  the 
Judgments  back  to  the  realities  from  which  they  originally 
sprang,  or,  at  least,  to  the  primitive  cognitions  brought  to 
Thought  by  the  proper  Presentative  Faculties. 

In  our  endeavors  to  realize  a  concept,  that  is,  to  ascertain 
How  to  real-    what  exactly  of  reality  it  expresses,  what  in  the 

ize  a  Con-  .  _        .  ,  .  . 

cept.  reality  ot  things  around  exactly  corresponds  to  it, 

how  far  and  in  what  respects  it  is  a  true,  trustworthy  cogni- 
tion of  the  realities  to  which  it  applies,  we  must  not  expect 
of  course  to  find  an  object  that  is  exactly  commensurate  with 


CONCEPTS.  67 

the  Concept ;  that  is,  an  aggregation  of  just  so  many  sub- 
jects, no  more,  no  less,  having  the  single  predicate  under 
which  we  have  found  the  Concept,  or  an  aggregation  of  just 
so  many  attributes  belonging  to  the  single  subject  under 
which  they  are  conceived  or  brought  together  in  thought. 
We  must  not  expect,  for  instance,  when  we  endeavor  to 
realize  the  Concept,  Man,  to  find  an  object  that  is  rational 
and  animal,  nothing  more,  nothing  le.-s ;  —  an  object  that 
is  merely  rational,  with  no  attributes  that  determine  this 
rationality  more  specifically  —  an  object,  for  instance,  that  is 
not  learned  nor  unlearned,  prince  nor  savage  ;  that  is  not  tall 
nor  short,  black  nor  white,  male  nor  female.  The  Concept 
did  not  arise,  was  not  formed,  in  such  a  way  as  to  authorize 
any  such  expectation.  It  was  founded  immediately,  as  we 
have  seen,  in  a  plurality  of  judgments ;  and  these  judgments 
were  formed  from  what  was  presented  to  the  thought.  If 
this  datum  to  the  thought  be,  for  example,  supposed  to  have 
been  presented  by  the  Faculty  of  Perception,  and  the  move- 
ment of  Thought  to  have  been  from  the  whole  to  the  parts, 
then,  as  we  have  seen,  Thought  took  the  datum  as  a  whole, 
say  Socrates,  and  one  of  its  parts,  say  the  composite  attribute, 
rational  animal,  and  affirmed  this  part  of  the  whole,  thus, 
Socrates  is  rational  animal,  leaving  out  of  regard  for  the 
time,  all  other  attributes  or  parts,  as  that  he  was  learned, 
modest,  tall,  white,  and  the  like.  Other  data,  as  Cicero, 
James,  were  presented  and  treated  in  the  same  way.  Then 
these  several  judgments  being  thus  in  the  mind,  and  having 
the  same  predicate,  which  was  one  of  the  many  attributes 
originally  given  in  the  several  subjects,  Socrates,  &c,  were 
synthesized  or  aggregated,  and  the  common  predicate  and 
copula  being  dropped,  we  attained  the  Concept,  which  we 
signalized  in  language  as  a  unit,  by  the  term  Man.  Now 
the  only  element  of  reality  introduced  by  this  process  into 
the  Concept  is  simply  the  attribute  rational  animal,  given  in 
the  plurality  of  subjects,  Socrates,  Cicero,  James.  All  of 
real,  therefore,  that  we  can  expect  to  find  in  our  endeavor 


68  PURE  LOGIC. 

to  realize  the  Concept,  Man,  is  simply  rational  animal.  This 
complex  attribute,  if  the  Concept  is  valid,  must  be  found, 
must  be  realized,  in  every  subject  embraced  under  the  Con- 
cept in  Socrates,  Cicero,  James,  &c. ;  but  it  would  be  absurd 
to  expect  more  as  necessarily  expressed  by  the  Concept,  un- 
less the  attribute  under  which  as  its  necessary  Base  the  Con- 
cept was  formed  as  being  identical  in  the  plurality  of  subjects, 
embraced  something  more  than  rational  animal. 

Inasmuch  as  words  expressing  Concepts  make  up  a  great 
majority  of  the  terms  in  use  in  language,  it  becomes  an  in- 
teresting question,  how  far  and  on  what  grounds  we  may 
assume  such  words  to  denote  real  objects.  And,  although 
the  question  in  its  full  import  transcends  the  proper  sphere 
of  logical  science,  yet  as  the  exposition  we  have  given  of  the 
genesis  of  the  Concept  enables  us  to  indicate  the  conditions 
of  such  a  correspondence,  and  as  some  knowledge  of  them  is 
necessarily  involved  in  logical  methodology,  where  the  ques- 
tion will  again  meet  us,  it  may  be  proper  here  in  a  very  sum- 
mary way  to  indicate  them. 

1.  The  original  datum  to  thought  must  be  a  true  presenta- 
tion of  the  real  object,  and  this  implies  two  things:  (1) 
that  objective  reality  may  be  apprehended  by  the  human 
mind ;  and  (2)  that  the  mind  rightly  apprehends  it. 

2.  The  objective  world  must  have  in  its  parts  likenesses 
or  resemblances  corresponding  to  the  identities  recognized  in 
forming  the  Concept.  This  condition  implies  (1)  that  the 
objective  world  has  parts  corresponding  to  those  apprehended 
in  thought ;  (2)  that  these  parts  are  in  some  respects  identi- 
cal one  with  another ;  and  (3)  that  the  identities  recognized 
in  Thought,  in  the  Concept,  are  the  same  as  those  that  exist 
in  the  real  objects  of  thought. 

In  all  thinking,  and  especially  in  all  communication  of 
thought,  in  all  discourse,  there  are  three  elements  which  it  is 
ever  necessary  to  discriminate  with  careful  vigilance.  There 
are,  first,  the  objects  of  which  we  think  or  speak  ;  secondly, 
our  cognitions  or  mental  apprehensions  of  those  objects  ;  and, 


CONCEPTS.  69 

thirdly,  the  words  in  which  these  cognitions  of  these  objects 
of  our  thought  are  expressed.  Thought  thus  stands  in  a 
twofold  relation  to  its  object,  and  to  its  expression  or  embodi- 
ment ;  and  there  is  accordingly  a  twofold  liability  to  error, 
as  we  may,  in  the  first  place,  confound  our  thoughts,  our 
cognitions,  with  the  objects  of  which  we  think  ;  or,  in  the 
second  place,  confound  these  cognitions  with  the  words  in 
which  they  are  expressed. 

In  respect  to  this  second  relation  of  thought,  its  relation 
to  language,  their  reciprocal  dependence  on  each  other,  and 
the  imperfection  of  thought  by  reason  of  this  dependence, 
the  following  general  observations  of  Sir  William  Hamilton 
are  particularly  worthy  of  attention  :  — 

"  For  Perception,  indeed,  for  the  mere  consciousness  of 
the  similarities  and  dissimilarities  in  the  objects  perceived, 
for  the  apprehension   of   the  causal  connection  of    certain 
things,  and  for  the  application  of  this  knowledge  to  the  at- 
tainment of  certain  ends,  no  language  is  necessary;  and  it  is 
only  the  exaggeration  of  a  truth  into  an  error,  when  philos- 
ophers maintain  that  language  is  the  indispensable  condition 
of  even  the  simpler  energies  of  knowledge.      Language  is 
the  attribution  of  signs  to  our   cognitions  of  things.     But  as 
a  cognition  must  have  been  already  there,  before  it  could  re- 
ceive a  sign,  consequently  that  knowledge  which  is  denoted 
by  the  formation  and  application  of  a  word  must  have  pre- 
ceded the  symbol  which  denotes  it.     Speech  is  thus  not  the 
mother,  but  the  godmother,  of  knowledge.     But  though,  in 
general,  we  must  hold  that  language,  as  the  product  and  cor- 
relative of  thought,  must  be  viewed  as  posterior  to  the  act 
of  thinking  itself;  on  the  other  hand,  it  must  be  admitted, 
that  we   could  never  have  risen  above  the  very  lowest  de- 
grees in  the  scale  of  thought,  without  the  aid  of  signs.     A 
sign  is  necessary  to  give  stability  to  our  intellectual  progress 
—  to  establish  each  step  in  our  advance  as  a  new  starting- 
point  for  our  advance  to  another  beyond. 

"  A  country  may  be  overrun  by  an  armed  host,  but  it  is 


70  PURE  LOGIC. 

only  conquered  by  the  establishment  of  fortresses.  Words 
are  the  fortresses  of  thought.  They  enable  us  to  realize  our 
dominion  over  what  we  have  already  overrun  in  thought ;  to 
make  every  intellectual  conquest  the  basis  of  operations  for 
others  still  beyond.  Or  another  illustration  :  All  have  heard 
of  the  process  of  tunneling,  of  tunneling  through  a  sand- 
bank. In  this  operation  it  is  impossible  to  succeed,  unless 
every  foot,  nay  almost  every  inch  in  our  progress,  be  secured 
by  an  arch  of  masonry,  before  we  attempt  the  excavation  of 
another.  Now,  language  is  to  the  mind  precisely  what  the 
arch  is  to  the  tunnel.  The  power  of  thinking  and  the  power 
of  excavation  are  not  dependent  on  the  word  in  the  one  case, 
or  the  mason-work  in  the  other  ;  but  without  these  subsidia- 
ries, neither  process  could  be  carried  on  beyond  its  rudiment- 
ary commencement.  Though,  therefore,  we  allow  that  every 
movement  forward  in  language  must  be  determined  by  an 
antecedent  movement  forward  in  thought ;  still,  unless  thought 
be  accompanied  at  each  point  of  its  evolution  by  a  corre- 
sponding evolution  of  language,  its  further  development  is 
arrested.  Thus  it  is,  that  the  higher  exertions  of  the  higher 
faculty  of  Understanding — the  classification  of  the  objects 
presented  and  represented  by  the  subsidiary  powers  in  the 
formation  of  a  hierarchy  of  notions,  the  connection  of  these 
notions  into  judgments,  the  inference  of  one  judgment  from 
another,  and,  in  general,  all  our  consciousness  of  the  rela- 
tions of  the  universal  to  the  particular,  consequently  all 
science  strictly  so  denominated,  and  every  inductive  knowl- 
edge of  the  past  and  future  from  the  laws  of  nature  —  not 
only  these,  but  all  ascent  from  the  sphere  of  sense  to  the 
sphere  of  moral  and  religious  intelligence,  are,  as  experience 
proves,  if  not  altogether  impossible  without  a  language,  at 
least  possible  to  a  very  low  degree. 

"  Admitting  even  that  the  mind  is  capable  of  certain  ele- 
mentary concepts  without  the  fixation  and  signature  of  lan- 
guage, still  these  are  but  sparks  which  would  twinkle  only  to 
expire  ;  and  it  requires  words  to  give  them  prominence,  and, 


CONCEPTS.  71 

by  enabling  us  to  collect  and  elaborate  them  into  new  con- 
cepts, to  raise  out  of  what  would  otherwise  be  only  scattered 
and  transitory  scintillations  a  vivid  and  enduring  li^ht. 

"  As  a  notion  or  concept  is  the  factitious  whole  or  unity 
made  up  of  a  plurality  of  subjects  or  of  attributes  —  a  whole 
too  often  of  a  very  complex  multiplicity  ;  and  as  this  multi- 
plicity is  only  mentally  held  together,  inasmuch  as  the  con- 
cept is  fixed  and  ratified  in  a  sign  or  word ;  it  frequently 
happens  that,  in  its  employment,  the  word  does  not  suggest 
the  whole  amount  of  thought  for  which  it  is  the  adequate 
expression,  but,  on  the  contrary,  we  frequently  give  and  take 
the  sign,  either  with  an  obscure  or  indistinct  consciousness  of 
.  its  meaning,  or  even  without  an  actual  consciousness  of  its 
signification  at  all.     In  consequence  of  this,  when  a  notion  is 
of  a  very  complex  and  heterogeneous  composition,  we  are 
frequently  wont  to  use  the  term  by  which  it  is  denoted,  with- 
out a  clear  or  distinct  consciousness  of  the  various  characters 
of  which  the  notion  is  the  sum  ;  and  thus  it  is,  that  we  both 
give  and  take  words  without  any,  or,  at  least,  without  the 
adequate  complement  of  thought.     In  countries  where  bank- 
notes have  not  superseded  the  use  of  the  precious  metals, 
large  payments  are  made  in  bags  of  money,  purporting  to 
contain  a  certain  number  of  a  certain  denomination  of  coin, 
or,  at  least,  a  certain  amount  in  value.     Now,  these  bags  are 
often  sealed  up  and  passed  from  one  person  to  another,  with- 
out the  tedious  process,  at  each  transference,  of  counting  out 
their  contents,  and  this  upon  the  faith  that,  if  examined,  they 
will  be  found  actually  to  contain  the  number  of  pieces  for 
which  they  are  marked,  and   for  which  they  pass   current. 
In  this  state  of  matters,  it  is,  however,  evident,  that  many 
errors  or  frauds  may  be  committed,  and  that  a  bag  may  be 
given  and   taken  in  payment  for  one  sum,  which   contains 
another,  or  which,  in  fact,  may  not  even  contain  any  money 
at  all.     Now  the  case  is  similar  in  regard  to  notions.     As  the 
sealed  bag  or  rouleau  testifies  to  the  enumerated  sum,  and 
gives  unity  to  what  would  otherwise  be  an  unconnected  mul- 


72  PURE  LOGIC. 

titude  of  pieces,  each  only  representing  its  separate  value  ;  so 
the  sign  or  word  proves  and  ratifies  the  existence  of  a  concept, 
that  is,  it  vouches  the  tying  up  of  a  certain  number  of  at- 
tributes or  characters  in  a  single  concept  —  attributes  which 
would  otherwise  exist  to  us  only  as  a  multitude  of  separate 
and  unconnected  representations  of  value.  So  far  the  anal- 
ogy is  manifest ;  but  it  is  only  general.  The  bag,  the  guar- 
anteed sum,  and  the  constituent  coins,  represent  in  a  still 
more  proximate  manner  the  term,  the  concept,  and  the  con- 
stituent characters.  For  in  regard  to  each,  we  may  do  one 
of  two  things.  On  the  one  hand,  we  may  test  the  bag,  that 
is,  open  it,  and  ascertain  the  accuracy  of  its  stated  value,  by 
counting  out  the  pieces  which  it  purports  to  contain  ;  or  we 
may  accept  and  pass  the  bag,  without  such  a  critical  enumer- 
ation. In  the  other  case,  we  may  test  the  general  term, 
prove  that  it  is  valid  for  the  amount  and  quality  of  thought 
of  which  it  is  the  sign,  by  spreading  out  in  consciousness  the 
various  characters  of  which  the  concept  professes  to  be  the 
complement ;  or  we  may  take  and  give  the  term  without 
such  an  evolution. 

"  It  is  evident  from  this,  that  notions  or  concepts  are  pecu- 
liarly liable  to  great  vagueness  and  ambiguity,  and  that  their 
symbols  are  liable  to  be  passed  about  without  the  proper  kind, 
or  the  adequate  amount,  of  thought." 

§  40.  Inasmuch,  likewise,  as  a  Concept  is  in  its  essential 
nature  an  aggregate  resulting  from  the  synthesis 

A  Concept  is  °°      o  o  J 

a  Quantity.  0f  tne  subjects  or  of  the  predicates  in  several  Judg- 
ments, it  is  necessarily  to  be  regarded  as  a  Quantity.  And 
in  this,  its  most  essential  characteristic,  we  are  to  find  the 
highest  principle  of  Division  in  the  distribution  of  Concepts. 
But  inasmuch  as  a  Concept  may  be  a  synthesis  of  Subjects  or 
of  Predicates,  we  have  at  once  given  us  the  primary  distinc- 
tion of  Concepts  into  the  two  classes  of  Subject-Concepts  and 
Predicate-Concepts.  These  two  kinds  of  Quantity  have  been 
denominated  by  logicians  Extensive  Quantity  and  Compre- 
hensive or  Intensive  Quantity  ;  Extensive  Quantity  belong- 


CONCEPTS.  73 

ing  to  concepts  in  so  far  as  formed  of  subjects,  and  Compre- 
hensive Quantity  belonging  to  them  in  so  far  as  they  are 
formed  of  predicates. 

§  41.  The  Extensive  Quantity  of  a  concept,  other- 
wise called  iis  Extension,  also  its  sphere  or  domain,  Extensive 
splicer  a,  regio,  quantitas,  ambitus,  and  by  the  Quantity- 
Greek  logicians,  its  breadth  or  latitude,  7rXdros,  respects  the 
concept  as  a  complement  of  subjects.  Thus  the  concept, 
man,  taken  in  its  Extensive  Quantity,  denotes  the  aggregate 
of  the  individual  subjects  of  which  some  common  attributes 
may  have  been  predicated  in  Judgments  actually  or  impliedly 
made  before,  as  Socrates,  Cicero,  James,  and  all  other  indi- 
viduals judged  as  rational  animal. 

In  this  Quantity  the  relation  of  the  concept  as  a  whole  to 
the  particular  subjects  which  are  its  component  parts,  is  ex- 
pressed by  the  preposition  under ;  thus,  Socrates  is  said  to 
be  contained  under  the  concept,  man. 

§  42.    The    Comprehensive    Quantity   of   a    concept, 
otherwise  called  its  Intensive  or  Internal   Quan-   comprehen- 
tity,  its  Comprehension,  Intension,  quantitas  com-  tensive111" 
plexus,  also  by  the  Greek  logicians  depth,  (3d8o<;,   Quantity, 
respects  the  concept  as  a  complement  of  predicates  or  attri- 
butes ;  as  thus  the  concept,  man,  taken  in  its  Comprehensive 
Quantity,  denotes  the  aggregate  of  the   attributes  that  may 
have  been  predicated  of  the  same  subject  in  former  actual  or 
implied  Judgments,  as  rational  and  animal,  attributed  sever- 
ally to  the  same  subject,  Socrates. 

In  this  Quantity,  the  relation  of  the  concept  as  a  whole 
to  the  particular  attributes  which  are  its  component  parts,  is 
expressed  by  the  preposition  in  ;  thus  the  concept,  man,  is 
said  to  contain  in  it  the  attribute  rational. 

§  43.  Nothing  in  the  formation  of  a  concept  forbids  a 
synthesis  of  terms  that  are  themselves  concepts. 

r.M  ...  ,  ...,.,         Amplifica- 

lhe  primitive    concepts,  as   the   primitive  Judg-   tion  of  Con- 
ments,  must  be  of  terms  that  are  individual ;  but  ctp 
these  terms  may  be  combined  with  other  individual  terms  or 


74  PUKE  LOGIC. 

with  concepts,  or  concepts  may  be  combined  with  other  con- 
cepts, and  in  either  quantity,  the  Base  ever  remaining  un- 
changed. 

The  logical  process  by  which  a  term  is  amplified  by  being 
combined  with  other  analogous  terms,  if  in  Extensive  Quan- 
tity, is  called  Generalization  ;  if  in  Comprehensive  Quantity, 
it  is  called  Determination. 

This  process  of  amplifying  a  term  or  concept,  may  be  thus 
exemplified.  We  will  begin  with  a  primitive  consciousness  in 
which  an  object  of  sight,  say  the  Moon,  is  brought  into  it. 
The  Judgment,  when  this  cognition  given  by  the  Faculty  of 
Perception  and  the  Intuitive  Cognition  of  Existence  occa- 
sioned by  the  perception,  present  themselves  before  its  view, 
at  once  affirms  Existence  both  of  the  subject  perceiving  — 
the  Ego  —  and  also  of  the  object  perceived,  I  am,  The.  moon 
is,  the  verb  being  used  here  substantively  to  include  both  the 
copula  and  the  predicate  of  Existence.  Under  the  common 
predicate,  the  subjects  may  be  synthesized,  and  a  concept 
emerges,  which,  by  successive  syntheses  of  subjects,  becomes 
the  concept  being,  comprehending  all  objects  of  Thought 
which  agree  in  respect  of  this  predicate.  We  can  enlarge 
the  contents  of  this  concept  taken  in  its  Extensive  Quantity, 
by  bringing  into  it  or  under  it  any  other  subject  of  a  Judg- 
ment having  this  predicate  ;  but  we  can  add  no  existing 
subject  to  Being  so  as  to  form  a  higher  class  of  subjects. 
We  cannot,  therefore,  amplify  the  concept  being,  so  that  it 
shall  become  a  higher  genus.  The  limit  to  the  amplification 
of  a  subject-concept,  that  is,  of  a  concept  in  Extensive 
Quantity,  is  thus  a  perfectly  simple  predicate.  But  this 
predicate  may  be  amplified  if  we  find  a  subject  having  this 
and  some  other  predicate.  Thus  in  the  Judgments  The  Moon 
is  existing,  The  Moon  is  material,  by  combining  the  predicates 
there  emerges  the  predicate-concept  Material  Existence,  that 
is,  Matter.  We  may  go  on  to  amplify  this  concept,  taken  in 
Comprehensive  Quantity,  by  combining  with  it  under  seme 
common  subject   another  predicate,  as  luminous,  and,  still 


CONCEPTS.  75 

further,  by  adding  to  this  new  amplification,  the  predicate 
by  reflection,  till  we  reach  the  limit  of  amplification  in  this 
direction.  It  is  obvious  that  as  we  thus  amplify  the  com- 
prehension of  the  concept,  we  are  contracting  the  bounda- 
ries of  the  subject  of  which  the  concept  may  be  affirmed,  that 
is,  we  are  determining  it.  Thus  existence  may  be  predi- 
cated of  many  objects  ;  material,  of  fewer ;  luminous,  of  fewer 
still ;  luminous  by  reflection,  of  yet  fewer  objects.  The  proc- 
ess of  amplifying  the  comprehension  is  called,  therefore, 
Determination,  as  logical  nomenclature  has  originated  rather 
from  the  view  of  objects  in  their  Extensive  Quantity.  It  is 
also  called  Concretion. 

On  the  other  hand,  if  we  begin  with  a  subject  having  not 
a  simple  predicate  as  before,  but  one  more  or  less  amplified, 
we  may  amplify  the  Extension  of  this  subject  by  combining 
with  it  subjects  having  some  part  of  this  predicate  in  common. 
Thus  beginning  with  Socrates  in  any  Judgment  having  a 
predicate  not  absolutely  simple,  as  in  the  Judgment,  Socrates 
is  of  Athens,  we  may  add  subjects  in  Judgments  having  the 
same  predicate,  as,  Plato  is  of  Athens,  Alcibiades  is  of  Athens, 
Xenophon  is  of  Athens,  &c,  and  we  obtain  the  subject-concept 
Athenian,  embracing  under  it  many  individuals.  So,  again, 
by  combining  Athenian,  Theban,  Spartan,  under  the  common 
predicate  of  Greece  or  Gi'ecian,  we  amplify  the  Extension  still 
more,  that  is,  we  bring  more  subjects  under  it.  This  proc- 
ess, that  of  amplifying  the  Extension,  is  called  Generaliza~ 
tion. 

It  will  be  observed  that,  from  the  inadequacy  of  language 
to  signalize  all  the  modifications  of  Thought,  these  two  quan- 
tities, notwithstanding  they  differ  so  much,  are  not  always 
distinguished  by  peculiar  forms  of  verbal  expression.  Indeed, 
almost  every  term  may  be  used  indifferently  either  as  Subject 
or  as  Predicate,  and  accordingly  in  either  Comprehension  or 
Extension.  The  use  in  discourse  alone  can  ordinarily  indi- 
cate in  which  Quantity  the  term  is  used.  Individuals,  as 
such,  can  never,  indeed,  be  predicates,  except  in  Identical 


76  PUKE  LOGIC. 

Propositions ;  yet  Language  does  not  hesitate  at  its  will  to 
trample  upon  this  high  prerogative  of  individuality,  and  con- 
script it  into  the  ranks  of  its  predicates,  as  its  wants  require. 
It  makes  Alexander  to  serve  as  predicate  of  every  ambitious 
military  conqueror,  and  proceeds  thus  to  create  a  genus  of 
Alexanders — restoring  the  subject-character,  but  robbing  it 
of  the  individual  prerogative.  Hence  the  necessity  to  correct 
and  valid  Thought  of  a  careful  discrimination  of  this  twofold 
significance  of  a  term  denoting  a  concept. 

The  ability  to  be  acquired  only  by  intelligent  practice, 
readily,  and,  as  it  were,  instinctively,  to  distinguish  these  two 
quantities  in  the  import  of  concepts,  is  needed  in  order  to  the 
read)r  and  correct  interpretation  of  discourse ;  to  facile  criti- 
cism of  discourse,  also,  and  determination  of  its  conformity  to 
truth,  and  the  detection  and  exposure  of  error.  Discourse, 
moreover,  becomes  at  once  freighted  with  a  double  richness 
of  meaning  to  the  mind  practiced  and  skillful  in  this  discrim- 
ination. But  vastly  more  needful  is  this  dexterity  in  the 
construction  of  Discourse.  In  this  the  main  and  more  essen- 
tial labor  consists  in  the  right  unfolding  of  knowledge,  which 
for  the  most  part  is  laid  up  in  concepts.  To  unfold  concepts 
in  ignorance  of  their  twofold  quantity  is  not  only  difficult  and 
slow,  because  in  blindness  as  to  the  necessary  path  to  be  pur- 
sued, but,  also,  unavoidably  liable  to  confusion,  from  which  it 
lias  been  truly  said  it  is  more  difficult  for  truth  to  emerge 
than  from  absolute  error. 

It  is  pertinent  to  remark  in  this  connection  that  obviously 
common  nouns,  or,  as  they  might  more  properly  be  called, 
class  nouns,  are  as  really  abstractions  as  any  others.  They 
do  not  stand  for  any  actual  concrete  realities.  There  is,  as 
has  been  shown,  no  real  being  answering  to  the  concept  horse, 
having  the  characters  solid-hoofed,  non-ruminant,  mammal, 
and  no  others.  The  concept  is  a  mere  product  of  Thought, 
and  is  the  result  of  abstraction.  It  is  only  by  abstracting 
from  other  properties  or  characters,  and  thus  limiting  the 
attention  to  one  or  more,  that  we  can  form  a  thought  of  any 


CONCEPTS.  77 

class  of  subjects.  Thus  it  happens,  that  any  predicate,  as  it 
can  be  made  a  subject  in  a  Judgment,  so  can  be  a  class  noun. 
A  concrete  noun  can  differ  from  an  abstract  only  in  this  re- 
spect, that  in  its  use  it  is  treated  as  a  Subject-concept,  while 
an  abstract  noun  is  treated  as  a  predicate-concept. 

"  Such,  in  general,  is  what  is  meant  by  the  two  quantities 
of  concepts  —  their  Extension  and  Comprehension. 

§  44.  "  But  these  quantities  are  not  only  different,  they  are 
opposed,  and  so  opposed,  that  though  each  supposes  intensive 
the  other  as  the  condition  of  its  own  existence,  still,  ^  cfuanti- 
however,  within  the  limits  of  conjunct,  of  correl-  p^,darte0  op" 
ative  existence,  they  stand  in  an  inverse  ratio  to  each  other- 
each  other  —  the  maximum  of  the  one  being  the  minimum 
of  the  other. 

"A  notion  is  extensively  great  in  proportion  to  the  greater 
number,  and  extensively  small  in  proportion  to  the  smaller 
number  of  subjects  it  contains  under  it.  When  the  Exten- 
sion of  a  concept  becomes  a  minimum,  that  is,  when  it  con- 
tains no  other  notions  under  it,  it  is  called  an  individual. 

"A  notion  is  intensively  great  in  proportion  to  the  greater 
number,  and  intensively  small  in  proportion  to  the 

_  .        .  .  Law  regulat- 

smaller   number   of  determinations    or   attributes   ingthemut- 

nil  rt^li- 

contained  in  it.      Is  the  Comprehension  of  a  con-   tions  of  ex- 

.    .  ,,  •      .      ,.  .  •       tension    and 

cept   a  minimum,  that  is,  is  the   concept   one  in   comprehen- 
which   a  plurality  of  attributes  can  no  longer  be   SIon' 
distinguished,  it  is  called  simple  ;  whereas,  inasmuch  as  its 
attributes  still  admit  of  discrimination,  it  is  called  complex  or 
compound. 

"  These  two  quantities  stand  always  in  an  inverse  ratio  to 
each  other :  for  the  greater  the  Comprehension  of  a  concept, 
the  less  is  its  Extension  ;  and  the  greater  its  Extension  the 
less  its  Comprehension. 

"  When  I  take  out  of  a  concept,  that  is,  abstract  from  it  one 
or  more  of  its  attributes,  I  diminish  its  comprehen- 

m,  .  „  .,  .  Illustration. 

sion.     Thus,  when  from  the  concept,  man,  equiva- 


78  PURE  log  re. 

lent  to  rational  animal,  I  abstract  the  attribute  or  determi- 
nation rational,  I  lessen  its  internal  quantity.  But  by  this 
diminution  of  its  comprehension  I  give  it  a  wider  extension  ; 
for  what  remains  is  the  concept,  animal,  and  the  Concept 
animal  embraces  under  it  a  far  greater  number  of  subjects 
than  the  concept  man" 

§  45.  Concepts  have  been  characterized  by  certain  relations 
_,   .  which  they  bear  to  one   another.     The  most  im- 

Eeciprocal  •; 

Relations  of    portant  of  the  different  kinds  of  concepts  as  thus 

Concepts.  ?  .       ...  .    . 

determined  will  best  be  exhibited  separately  under 
the  two  kinds  of  Quantity. 

"  As  dependent  upon  Extension,  concepts  stand  to  each 
Under  Ex-  other  in  the  five  mutual  relations  :  1°.  Of  Exclu- 
tension.  aon  ;  2°.  Of  Coextension  ;  3°.  Of  Subordination  ; 

4°.  Of  Coordination  ;  and  5°.  Of  Intersection. 

"  1.  One  concept  excludes  another  when  no  part  of  the 
one  coincides  with  any  part  of  the  other.  2.  One  concept  is 
coextensive  with  another,  when  each  has  the  same  subordi- 
nate concepts  under  it.  3.  One  concept  is  subordinate  to 
another  (which  may  be  called  the  Superordinate)  when  the 
former  is  included  within,  or  makes  a  part  of,  the  sphere  or 
extension  of  the  latter.  4.  Two  or  more  concepts  are  coor- 
dinated, when  each  excludes  the  other  from  its  sphere,  but 
when  both  go  immediately  to  make  up  the  extension  of  a 
third  concept,  to  which  they  are  co-subordinate.  5.  Concepts 
intersect  each  other,  when  the  sphere  of  the  one  is  partially 
contained  in  the  sphere  of  the  other. 

"  Of  Exclusion,  horse,  syllogism,  are  examples  :  there  is  no 
absolute  exclusion. 

"  As  examples  of  Coextension  —  the  concepts  living  being, 
Examples  of  and  organized  being,  may  be  given.  For,  using 
nai relations  the  term  life  as  applicable  to  plants  as  well  as  ani- 
inExten-eptS  niaH  there  is  nothing  living  which  is  not  organ- 
don,  ized,  and  nothing  organized  which  is  not  living. 
This  reciprocal  relation  will  be  represented  by  two  circles 
covering  each  other,  or  by  two  lines  of  equal  length  and  in 
positive  relations. 


CONCEPTS.  79 

"As  examples  of  Subordination  and  Coordination — man, 
dog,  horse,  stand,  as  correlatives,  in  subordination  to  the  con- 
cept animal,  and,  as  reciprocal  correlatives,  in  coordination 
with  each  other. 

"  What  is  called  the  reciprocal  relation  of  Intersection, 
takes  place  between  concepts  when  their  spheres  cross  or  cut 
each  other,  that  is,  fall  partly  within,  partly  without  each 
other.  Thus,  the  concept  black  and  the  concept  heavy  mu- 
tually intersect  each  other,  for  of  these  some  black  things 
are  heavy,  some  not,  and  some  heavy  things  are  black,  some 
not. 

"  Of  these  relations,  those  of  Subordination  and  Coordina- 
tion are  of  principal  importance,  as  on  them  reposes  the 
whole  system  of  classification  ;  and  to  them  alone  it  is,  there- 
fore, necessary  to  accord  a  more  particular  consideration. 

"  Under  the  Subordination  of  notions,  there  are  various 
terms  to  express  the  different  modes  of  this  relation  ;  these  it 
is  necessary  to  bear  in  mind,  for  they  form  an  essential  part 
of  the  language  of  Logic,  and  will  come  frequently,  in  the 
sequel,  to  be  employed  in  considering  the  analysis  of  Reason- 
ings. 

§  46.  "  Of  notions  which  stand  to  each  other  in  the  rela- 
tions of  Subordination  —  the  one  is  the  Hiqher  or 

ci  •        /         •  •     x       ,  Superior  and 

superior  (notw,  conceplus,  superior),  the  other  the   interior, 

ZT  r     •         /■      j  •  .  •     /•     •  Broader  and 

ower   or    Inferior    (notio,    conceptus,    inferior).   Narrower, 

The  superior  notion  is  likewise  called  the  Wider   NotI0DS" 
or  Broader  (latior),  the  inferior  is  likewise  called  the  Nar- 
rower (angustior). 

"  A  notion  is  called  the  higher  or  superior,  inasmuch  as  it 
is  viewed  as  standing  over  another  in  the  relation  of  subor- 
dination—  as  including  it  within  its  domain  or  sphere;  and 
a  correlative  notion  is  called  the  lower  or  inferior,  as  thus 
standing  under  a  superior.  Again,  the  higher  notion  is  called 
the  wider  or  broader,  as  containing  under  it  a  greater  num- 
ber of  things ;  the  lower  is  called  the  narrower,  as  contain- 
ing under  it  a  smaller  number. 


80  PURE  LOGIC. 

"  The  higher  or  wider  concept  is  called,  also,  in  contrast  to 
the   lower   or  narrower,  a  Universal  or   General 

Universal  <  . 

and  Particu-   Notion  (vorjp.0.  kol6o\ov,  notio,  conceptus,  universa- 

lar  Notions.       7 .  , .  x         .       . 

lis,  generalis)  ;  the  lower  or  narrower  concept,  m 
contrast  to  the  higher  or  wider,  a  Particular  Notion  (I'owixa. 
fxcptKov,  notio,  conceptus,  particularis). 

"A  notion  is  called  universal,  inasmuch  as  it  is  considered 
as  binding  up  a  multitude  of  parts  or  inferior  concepts  into 
the  unity  of  a  whole  ;  for  universus  means  in  unum  versus, 
or  ad  unum  versus,  that  is,  many  turned  into  one,  or  many 
regarded  as  one,  and  universal  is  employed  to  denote  the 
attribution  of  this  relation  to  objects.  A  notion  is  called 
particular,  inasmuch  as  it  is  considered  as  one  of  the  parts  of 
a  higher  concept  or  whole. 

"A  superior  concept  is  also  called  a  General  Notion  (yoqfta 
Genus  and  xaOoXov,  notio,  conceptus,  generalis),  or,  in  a  single 
Species.  word,  a    Genus   (yeVos,  genus)  :    and    an   inferior 

concept,  contained  under  a  higher,  is  called  a  Special  Notion 
(yorj/xa  elStKov,  notio,  conceptus,  specicdis),  or,  in  a  single  word, 
a  Species  (elSos,  species).  The  abstraction  which  carries  up 
species  into  genera,  is  called,  in  that  respect,  Generalization. 
The  determination  which  divides  a  genus  into  its  species  is 
called,  in  that  respect,  Specification.  Genera  and  Species 
are  both  called  Classes  ;  and  the  arrangement  of  things  under 
them  is,  therefore,  Classification. 

"  It  is  manifest  that  the  distinction  into  Genera  and  Spe- 
cies is  a  merely  relative  distinction :  as  the  same 

The  distinc-  .  J 

tion  of  Genus   notion  is,  in  one  respect,  a  genus,  in  another  re- 

and    Species  _,,  .  , 

merely  reia-  spect,  a  species.  b  or  except  a  notion  has  no 
higher  notion,  that  is,  except  it  be  itself  the  widest 
or  most  universal  notion,  it  may  always  be  regarded  as  sub- 
ordinated to  another ;  and,  in  so  far  as  it  is  actually  thus  re- 
garded, it  is  a  -species.  Again,  every  notion,  except  that 
which  has  under  it  only  individuals,  is,  in  so  far  as  it  is 
thus  viewed,  a  genus.  For  example,  the  notion,  triangle, 
if  viewed  in  relation  to  the  notion  of  rectilineal  figure,  is  a 


CONCEPTS.  81 

species,  as  is  likewise  rectilineal  figure  itself,  as  viewed  in 
relation  to  figure  simply.  Again,  the  concept  triangle  is  a 
genus,  when  viewed  in  reference  to  the  concepts  —  rigid- 
angled  triangle,  acute-angled  triangle,  etc.  A  right-angled 
triangle  is,  however,  only  a  species,  and  not  possibly  a  genus, 
if  under  it  be  necessarily  included  individuals  alone.  But, 
in  point  of  fact,  it  is  impossible  to  reach  in  theory  any  lowest 
species;  for  we  can  always  conceive  some  difference  by 
which  any  concept  may  be  divided  ad  infinitum.  This,  how- 
ever, as  it  is  only  a  speculative  curiosity,  like  the  infinites- 
imal divisibility  of  matter,  may  be  thrown  out  of  view  in  re- 
lation to  practice  ;  and,  therefore,  the  definition,  by  Porphyry 
and  logicians  in  general,  of  the  lowest  species,  is  practically 
correct,  even  though  it  cannot  be  vindicated  against  theoret- 
ical objections.  On  the  other  hand,  we  soon  and  easily  reach 
the  highest  genus,  which  is  given  in  to  oV,  ens  aliquid,  being, 
thing,  something,  etc.,  which  are  only  various  expressions  of 
the  same  absolute  universality. 

u  In  regard  to  the  terms  Generalization  and  Specification, 
these  are  limited  expressions  for  the  processes  of  Generifica- 
Abstraction  and  Determination,  considered  in  a  s^fgj1^ 
particular  relation.  And  first,  in  regard  to  Ab-  —what, 
straction  and  Generification.  In  every  complex  notion,  we 
can  limit  our  attention  to  its  constituent  characters,  to  the  ex- 
clusion of  some  one.  We  thus  think  away  from  this  one  — 
we  abstract  from  it.  Now,  the  concept  which  remains,  that 
is,  the  fasciculus  of  thought  minus  the  one  character  which 
we  have  thrown  out,  is  in  relation  to  the  original  —  the  entire 
concept,  the  next  higher  —  the  proximately  superior  notion. 
But  a  concept  and  a  next  higher  concept  are  to  each  other  as 
species  and  genus.  The  process  of  Abstraction,  therefore, 
by  which  out  of  a  proximately  lower,  Ave  evolve  a  proxi- 
mately higher,  concept,  is,  when  we  speak  .with  logical  pre- 
cision, called  the  process  of  Generalization. 

"  Take,  for  example,  the  concept,  man.     This  concept  is 
proximately  composed  of  the  two  concepts   or  constituent 
6 


82  PURE  LOGIC. 

characters  —  animal  and  rational  being.  If  we  think  either 
of  these  characters  away  from  the  other,  we  shall  have  in 
that  other  a  proximately  higher  concept,  to  which  the  con- 
cept man  stands  in  the  relation  of  a  species  to  its  genus. 
If  we  abstract  from  animal,  then  man  will  stand  as  a  species 
in  subordination  to  the  genus,  rational  being,  and  the  concept, 
animal,  will  then  afford  only  a  difference  to  distinguish  man 
as  a  coordinate  species  from  immaterial  intelligences.  If,  on 
the  other  hand,  we  abstract  from  rational  being,  then  man 
will  stand  as  a  species  in  subordination  to  the  genus  animal, 
having  for  a  coordinate  species,  irrational  animal.  Such  is 
the  process  of  Generalization.  Now -for  the  converse  process 
of  Specification. 

"  Every  series  of  concepts  which  has  been  obtained  by 
abstraction,  may  be  reproduced  in  an  inverted  order,  when, 
descending  from  the  highest  notion,  we  step  by  step  add  on 
the  several  characters  from  which  we  had  abstracted  in  our 
ascent.  This  process,  as  has  been  stated,  is  called  Determi- 
nation —  a  very  appropriate  expression,  inasmuch  as  by  each 
character  or  attribute  which  we  add  on,  we  limit  or  deter- 
mine, more  and  more,  the  abstract  vagueness  or  extension  of 
the  notion  ;  until,  at  last,  if  every  attribute  be  annexed,  the 
sum  of  attributes  contained  in  the  notion  becomes  convertible 
with  the  sum  of  attributes  of  which  some  concrete  individual 
or  reality  is  the  complement.  Now,  when  we  determine  any 
notion  by  adding  on  a  subordinate  concept,  we  divide  it ;  for 
the  extension  of  the  higher  concept  is  precisely  equal  to  the 
extension  of  the  added  concept  plus  its  negation.  Thus,  if 
to  the  concept,  animal,  we  add  on  the  next  lower  concept, 
rational,  we  divide  its  extension  into  two  halves  —  the  one 
equal  to  rational  animal,  the  other  equal  to  its  negation, 
that  is,  to  irrational  animal.  Thus  an  added  concept  and  its 
negation  always  constitute  the  immediately  lower  notion,  into 
which  a  higher  notion  is  divided.  But  as  a  notion  stands  to 
the  notions  proximately  subordinate  to  it  in  the  immediate 
relation  of  a  genus  to  its  species,  the  process  of  Determina- 


CONCEPTS.  83 

tion,  by  which  a  concept  is  thus  divided,  is,  in  logical  lan- 
guage, appropriately  denominated  Specification. 

"  So  much  in  general  for  the  Subordination  of  notions, 
considered  as  Genera  and  Species.  There  are,  however, 
various  gradations  of  this  relation,  and  certain  terms  by 
which  these  are  denoted.  The  most  important  of  these  are 
comprehended  in  the  following  paragraph. 

§  47.  "  A  Genus  is  of  two  degrees  —  a  highest  and  a  lower. 
In  its  highest  degree,  it  is  called  the  Supreme  or 

°  /    ,  ,  Gradations 

Most  General  Genus  (yevos  yeviKwraroi',  genus  sum-   of  Genera 
mum,  or  generalissimum),  and   is    defined,  'that  and  their 

i  •  -i     i     •  ,.  .       ,    designations. 

which  being;  a  genus  cannot  become  a  species. 


s 


In  its  lower  degree,  it  is  called  a  Subaltern  or  Intermediate 
(yeVos  vTrdXXrjXoy,  genus  subalternum  or  medium),  and  is  de- 
fined, '  that  which  being  a  genus  can  also  become  a  species.' 
A  Species,  also,  is  of  two  degrees  —  a  lowest  and  a  higher. 
In  its  lowest  degree,  it  is  called  a  Lowest  or  Most  Special 
Species  (elSos  ci8ikojto.tov,  species  infima,  ultima,  or  specialis- 
sima),  and  is  defined,  '  that  which  being  a  species  cannot  be- 
come a  genus.'  In  its  higher  degree,  it  is  called  a  Subalter?i 
or  Intermediate  Species  (e!8os  vTrdXXrjXov,  species  subalterna 
media),  and  is  defined,  '  that  which  being  a  species  may  also 
become  a  genus.'  Thus  a  Subaltern  Genus  and  a  Subaltern 
Species  are  convertible. 

"  These  distinctions  and  definitions  are  taken  from  the  cele- 
brated Introduction  of  Porphyry  to  the  Categories  of  Aris- 
totle, and  they  have  been  generally  adopted  by  logicians.  It 
is  evident  that  the  only  absolute  distinction  here  established 
is  that  between  the  Highest  or  Supreme  Genus  and  the  Low- 
est Species  ;  for  the  other  classes  —  to  wit,  the  Subaltern 
or  Intermediate  —  are,  all  and  each,  either  genera  or  species, 
according  as  we  regard  them  in  an  ascending  or  a  descending 
order  —  the  same  concept  being  a  genus,  if  considered  as  a 
whole  containing  under  it  inferior  concepts  as  parts,  and  a 
species,  if  considered  as  itself  the  part  of  a  higher  concept  or 
whole.     The  distinction  of  concepts  into  Genus  and  Species, 


84  PURE  LOGIC. 

into  Supreme  and  Intermediate  Genus,  into  Lowest  and  Inter- 
mediate Species,  is  all  that  Logic  takes  into  account;  because 
these  are  all  the  distinctions  of  degree  that  are  given  neces- 
sarily in  the  form  of  thought,  and  as  abstracted  from  all  de- 
terminate matter. 

"  It  may  be  remarked,  by  the  way,  that  in  the  physical 
sciences  of  arrangement,  the  best  instances  of  which  are 
seen  in  the  different  departments  of  Natural  History,  it  is 
found  necessary,  in  order  to  mark  the  relative  place  of  each 
step  in  the  ascending  and  descending  series  of  classes,  to 
bestow  on  it  a  particular  designation.  Thus  kingdom,  sub- 
kingdom,  class,  order,  tribe,  family,  genus,  subgenus,  species, 
subspecies,  variety,  and  the  like,  are  terms  that  serve  conven- 
iently to  mark  out  the  various  degrees  of  generalization,  in 
its  application  to  the  descriptive  sciences  of  nature. 

§  48.  "  The  character,  or  complement  of  characters,  by 
Generic  which  a  lower  genus  or  species  is  distinguished, 

indMduaT11  both  ^vom  ^ie  genus  to  which  it  is  subordinate,  and 
Difference.  from  the  other  genera  or  species  with  which  it  is 
coordinated,  is  called  the  Generic  or  the  Specific  Difference, 
Siacf)opa  yeviK-fj,  and  &ia<f>opa  eiSik^,  differentia  generica,  and 
differentia  specif  ca.  The  sum  of  characters,  again,  by  which 
a  singular  or  individual  thing  is  discriminated  from  the  spe- 
cies under  which  it  stands  and  from  other  individual  things 
along  with  which  it  stands,  is  called  the  Individual  or  Sin- 
gular or  Numerical  Difference  (differentia  individualis  vel 
singidaris  vel  numerica). 

"  Two  things  are  thus  said  to  be  generically  different,  inas- 
much as  they  lie  apart  in  two  different  genera ; 

Generic    and  .  .. 

Specific  Dif-  specifically  different,  inasmuch  as  they  lie  apart  in 
two  different  species ;  individually  or  numerically 
different,  inasmuch  as  they  do  not  constitute  one  and  the 
same  reality.  Thus,  animal  and  stone  may  be  said  to  be 
generically  different ;  horse  and  ox  to  be  specifically  different ; 
Highflyer  and  Eclipse  to  be  numerically  or  individually  dif- 
ferent.    It  is  evident,  however,  that  as  all  genera  and  species, 


-CONCEPTS.  85 

except  the  highest  of  the  one  and  the  lowest  of  the  other,  may 
be  styled  indifferently  either  genera  or  species,  generic  differ- 
ence and  specific  difference  are  in  general  only  various  ex- 
pressions of  the  same  thing;  and,  accordingly,  the  terms 
heterogeneous  and  homogeneous,  which  apply  properly  only  to 
the  correlation  of  genera,  are  usually  applied  equally  to  the 
correlation  of  species. 

"  Individual  existence  can  only  be  perfectly  discriminated 
in  Perception,  external  or  internal,  and  their  nu-        .  .     , 

*  .  Individual 

merical  differences  are  endless  ;  for  of  all  possible   or  singular 

Difference. 

contradictory  attributes,  the  one  or  the  other  must, 
on  the  principles  of  Disjunction  and  Excluded  Middle,  be 
considered  as  belonging  to  each  individual  thing.  On  the 
other  hand,  species  and  genera  may  be  perfectly  discrimi- 
nated by  one  or  few  characters.  For  example,  man  is  dis- 
tinguished from  every  genus  or  species  of  animal  by  the  one 
character  of  rationality  ;  triangle,  from  every  other  class  of 
mathematical  figures,  by  the  single  character  of  trilaterality. 
It  is,  therefore,  far  easier  adequately  to  describe  a  genus  or 
species  than  an  individual  existence ;  as  in  the  latter  case 
we  must  select,  out  of  the  infinite  multitude  of  characters 
which  an  individual  comprises,  a  few  of  the  most  prominent, 
or  those  by  which  the  thing  may  most  easily  be  recognized. 
But  as  those  which  we  thus  select  are  only  a  few,  and  are 
only  selected  with  reference  to  our  faculty  of  apprehension 
and  our  capacity  of  memory,  they  always  constitute  only  a 
petty,  and  often  not  the  most  essential  part  of  the  numerical 
differences  by  which  the  individuality  of  the  object  is  de- 
termined. 

§  49.  "  Notions,  in  so  far  as  they  are  considered  the  coor- 
dinate species  of  the  same  genus,  may  be  called      .. 
Conspccies  ;  and  in  so  far  as  Conspecies  are  con-   tion  of  Con- 

C6ptS. 

sidered  to  be  different  but  not  contradictory,  they 

are  properly  called  Discrete  or  Disjunct  Notions  (?wtiones 

discretce  vel  disjunctce). 

§  50.  "  The  whole  classification  of  things  by  Genera  and 


86  PURE  LOGIC. 

Species  is  governed  by  two  laws.  The  one  of  these,  the  law 
The  two  gen-  of  Homogeneity  (principium  Homogeneitatis),  is 
which  Sub-  —  That  how  different  soever  may  be  any  two  con- 
and  Coordi-  cepts,  they  both  still  stand  subordinated  under 
der  Ex'ten-  some  higher  concept ;  in  other  words,  things  the 
uTated— reS"  most  dissimilar  must,  in  certain  respects,  be  simi- 
■m.,  of  Ho-  ]ar      The  other,  the  law  of  Heteroqeneitv  (prin- 

mogeneity  &  j    \r 

andHetero-  cipium  Heterogeneitatis),  is  —  That  every  concept 
contains  other  concepts  under  it;  and,  therefore, 
when  divided  proximatelj',  we  descend  always  to  other  con- 
cepts, but  never  to  individuals ;  in  other  words,  things  the 
most  homogeneous  —  similar — must,  in  certain  respects,  be 
heterogeneous  —  dissimilar. 

"  Of  these  two  laws,  the  former,  as  the  principle  which  en- 
ables, and  in  fact  compels,  us  to  rise  from  species  to  genus,  is 
that  which  determines  the  process  of  Generifi cation  ;  and  the 
latter,  as  the  principle  which  enables,  and  in  fact  compels,  us 
to  find  always  species  under  a  genus,  is  that  which  regulates 
the  process  of  Specification.  The  second  of  these  laws,  it  is 
evident,  is  only  true  ideally,  only  true  in  theory.  The  infin- 
ite divisibility  of  concepts,  like  the  infinite  divisibility  of  space 
and  time,  exists  only  in  speculation.  And  that  it  is  theoret- 
ically valid,  will  be  manifest,  if  we  take  two  similar  concepts, 
that  is,  two  concepts  with  a  small  difference :  let  us  then 
clearly  represent  to  ourselves  this  difference,  and  we  shall 
find  that  how  small  soever  it  may  be,  we  can  always  conceive 
it  still  less,  without  being  nothing,  that  is,  we  can  divide  it  ad 
infinitum  ;  but  as  each  of  these  infinitesimally  diverging  dif- 
ferences affords  always  the  condition  of  new  species,  it  is 
evident  that  we  can  never  end,  that  is,  reach  the  individual, 
except  per  saltum. 

§  51.  "  When  two  or  more  concepts  are  compared  together 
identical        according  to  their  Comprehension,  they  either  co- 

and  Different    .      .  .   •        i  •  1  -i  i 

Notions.  incide  or  they  do  not ;  that  is,  they  either  do  or  do 
not  comprise  the  same  characters.  Notions  are  thus  divided 
into  Identical  and  Different  (conceptus  identici  et  diver  si). 


CONCEPTS.  87 

The  Identical  are  either  absolutely  or  relatively  the  same. 
Of  notions  Absolutely  Identical  there  are  actually  none  ;  no- 
tions Relatively  Identical  are  called,  likewise,  Similar  or  Cog- 
nate {notiones  similes,  affines,  cognatce) ;  and  if  the  common 
attributes,  by  which  they  are  allied,  be  proximate  and  neces- 
sary, they  are  called  Reciprocating  or  Convertible  {notiones 
reciprocce,  convertibles). 

"  In  explanation  of  this  paragraph,  it  is  only  necessary  to 
say  a  word  in  regard  to  notions  absolutely  Identi-   Absolutely 

Tflt-TltlOfLl 

cal.  That  such  are  impossible,  is  manifest.  For,  it  Notions  im- 
being  assumed  that  such  exist,  as  absolutely  iden-  possl 
tical,  they  necessarily  have  no  differences  by  which  they  can 
be  distinguished  :  but  what  are  indiscernible  can  be  known, 
neither  as  two  concepts  nor  as  two  identical  concepts ;  be- 
cause we  are,  ex  hypothesi,  unable  to  discriminate  the  one 
from  the  other.  They  are,  therefore,  to  us  as  one.  Notions 
absolutely  identical  can  only  be  admitted,  if,  abstracting  our 
view  altogether  from  the  concepts,  we  denominate  those  no- 
tions identical  which  have  reference  to  one  and  the  same 
object,  and  which  are  conceived  either  by  different  minds,  or 
by  the  same  mind,  but  at  different  times.  Their  difference  is, 
therefore,  one  not  intrinsic  and  necessary,  but  only  extrinsic 
and  contingent.  Taken  in  this  sense,  Absolutely  Identical 
notions  will  be  only  a  less  correct  expression  for  Reciprocat- 
ing or  Convertible  notions. 

§  52.  "  Considered  under  their  Comprehension,  concepts, 
a^ain,  in  relation  to  each  other,  are  said  to  be  opposition 
either  Congruent  or  Agreeing,  inasmuch  as  they  of  oncepts 
may  be  connected  in  thought ;  or  Conjlictive,  inasmuch  as 
they  cannot.  The  confliction  constitutes  the  Opposition  of 
notions  (to  avTLKelaOai,  oppositio).  This  is  twofold  :  1°. 
Immediate  or  Contradictory  Opposition,  called  likewise  Re- 
pugnance (to  di/ric/xiTiKoJS  avTu«u(r6ai,  dvTi<£ao-is,  oppositio 
immediata  sive  contradictoria,  repugnantia)  ;  and,  2°.  Me- 
diate or  Contrary  Opposition  (to  IvavTiwn  avTiKexaOai,  Ivav- 
TidVqs,  oppositio  mediata  vel  contraria).   The  former  emerges 


88  PURE  LOGIC. 

when  one  concept  abolishes  (tollit),  directly  or  by  simple 
negation,  what  another  establishes  (po?iit)  ;  the  latter,  when 
one  concept  does  this  not  directly  or  by  simple  negation,  but 
through  the  affirmation  of  something  else. 

"  Identity  is  not  to  be  confounded  with  Agreement  or  Con- 
identity  and  g™ence,  nor  Diversity  with  Confliction.  All  iden- 
Diversitent '  ^ca^  concePts  are>  indeed,  congruent ;  but  all  con- 
and  Conflic-  gruent  notions  are  not  identical.  Thus  learning, 
and  virtue,  beauty  and  riches,  magnanimity  and 
stature,  are  congruent  notions,  inasmuch  as,  in  thinking  a 
thing,  they  can  easily  be  combined  in  the  notion  we  form  of 
it,  although  in  themselves  very  different  from  each  other.  In 
like  manner,  all  conflicting  notions  are  diverse  or  different  no- 
tions, for  unless  different,  they  could  not  be  mutually  conflict- 
ive,  but  on  the  other  hand,  all  different  concepts  are  not 
conflictive,  but  those  only  whose  difference  is  so  great  that 
each  involves  the  negation  of  the  other ;  as,  for  example, 
virtue  and  vice,  beauty  and  deformity,  wealth  and  poverty. 
Thus  these  notions  are  by  preeminence  —  kclt  l&xqv  —  said 
to  be  opposed,  although  it  is  true  that,  in  thinking,  we  can 
oppose,  or  place  in  antithesis,  not  only  different,  but  even 
identical,  concepts. 

"  To  speak  now  of  the  distinction  of  Contradictory  and  Con- 
Contradic-  trary  Opposition,  or  of  Contradiction  and  Contra- 
Contrardo  -  r'ety  '  °^ tnese  t'ie  former,  Contradiction,  is  exem- 
position.  plified  in  the  opposites  —  yellow,  not  yellow  ;  walk- 
ing, not  walking.  Here  each  notion  is  directly,  immediately, 
and  absolutely  repugnant  to  the  other  —  they  are  reciprocal 
negatives.  This  opposition  is,  therefore,  properly  called  that 
of  Contradiction  or  of  Repugnance ;  and  the  opposing  no- 
tions themselves  are  contradictory  or  repugnant  notions  —  in 
a  single  word,  contradictories.  The  latter,  or  Contrary  Op- 
position, is  exemplified  in  the  opposites,  yellow,  blue,  red,  etc., 
walking,  standing,  lying,  etc. 

"  In  the  case  of  Contradictory  Opposition,  there  are  only  two 
conflictive  attributes  conceivable  :  and  of  these  one  or  other 


CONCEPTS.  89 

must  be  predicated  of  the  object  thought.  In  the  case  of 
Contrary  Opposition,  on  the  other  hand,  more  than  two  con- 
nective characters  are  possible,  and  it  is  not,  therefore,  neces- 
sary, that  if  one  of  these  be  not  predicated  of  an  object,  any 
one  other  must.  Thus,  though  I  cannot  at  once  sit  and 
stand,  and  consequently  sitting  and  standing  are  attributes 
each  severally  incompatible  with  the  other ;  yet  I  may  exist 
neither  sitting  nor  standing — I  may  lie ;  but  I  must  either 
sit  or  not  sit,  I  must  either  stand  or  not  stand,  etc.  Such, 
in  general,  are  the  oppositions  of  Contradiction  and  Contra- 
riety." 

§  53.  Concepts  as  compared  with  each  other  in  respect  of 
their  Comprehension,  are  further  distinguished  into  intrinsic 
Intrinsic  and  Extrinsic.  The  former  are  made  up  Notions- 
of  those  attributes  which  are  presented  to  Thought  as  its  view 
is  turned  from  the  object  inwardly  to  its  parts.  These  attri- 
butes are  of  the  proper,  inner  being  or  essence  of  the  object ; 
and,  severally  considered,  are  called  Essentials,  or  Internal 
Denominations  (oucriojcfy,  essentialia,  denominations  internee, 
intrinsic^),  and  conjunctly,  the  Essence  {ova-la,  essentia).  The 
latter,  on  the  contrary,  consist  of  those  attributes  which  are 
presented  to  thought  as  its  view  is  turned  outward  from  the 
object  to  other  objects  around.  These  attributes  of  external 
relation  are  styled  Accidents,  or  Extrinsic  Denominations 
(o-vfxficfi-qKOTa,  accidentia,  denominationes  externce  or  extrin- 
sicce). 

§  54.  "  Further,  in  respect  of  their  Comprehension,  no 
less  than  of  their  Extension,  notions  stand  to  each  involution 
other  in  a  relation  of  Containing  and  Contained  ;  nation?0"11" 
and  this  relation,  which,  in  the  one  quantity  (extension)  is 
styled  that  of  Subordination,  may  in  the  other  (comprehen- 
sion), for  distinction's  sake,  be  styled  that  of  Involution.  Co- 
ordination is  a  term  which  may  be  applied  in  either  quan- 
tity, being  the  relation  alike  in  both  of  Part  to  Complementary 
Part. 

"  In  the  quantity  of  comprehension,  one  notion  is  involved 


90  PURE  LOGIC. 

in  another,  when  it  forms  a  part  of  the  sum  total  of  charac- 
ters, which  together  constitute  the  comprehension  of  that  other ; 
and  two  notions  are  in  this  quantity  coordinated,  when,  while 
neither  comprehends  the  other,  both  are  immediately  com- 
prehended in  the  same  lower  concept. 

"  Thus  the  notion  of  the  individual  Socrates  contains  in  it, 
besides  a  multitude  of  others,  the  characters  of  son  of  Soph- 
roniscus,  Athenian,  Greek,  European,  man,  animal,  organ- 
ized being,  etc.  But  these  notions,  these  characters,  are  not 
all  equally  proximate  and  immediate  ;  some  are  only  given  in 
and  through  others.  Thus  the  character  Athenian  is  appli- 
cable to  Socrates  only  in  and  through  that  of  son  of  Sophro- 
niscus —  the  character  of  Greek,  only  in  and  through  that  of 
Athenian  —  the  character  of  European,  only  in  and  through 
that  of  Greek  —  and  so  forth  ;  in  other  words,  Socrates  is  an 
Athenian  only  as  the  son  of  Sophroniscus,  only  a  Greek  as 
an  Athenian,  only  a  European  as  a  Greek,  only  a  man  as  a 
European,  only  an  animal  as  a  man,  only  an  organized  being 
as  an  animal.  Those  characters,  therefore,  that  are  given  in 
and  through  others,  stand  to  these  others  in  relation  of  parts 
to  wholes  ;  and  it  is  only  on  the  principle  —  Part  of  the  part 
is  a  part  of  the  whole,  that  the  remoter  parts  are  the  parts 
of  the  primary  whole.  Thus,  if  we  know  that  the  individual 
Socrates  comprehends  the  character  son  of  Sophroniscus,  and 
that  the  character  son  of  Sophroniscus  comprehends  the  char- 
acter Athenian ;  we  are  then  warranted  in  saying  that  Soc- 
rates comprehends  Athenian,  in  other  words,  that  Socrates 
is  an  Athenian.  The  example  here  taken  is  too  simple  to 
show  in  what  manner  our  notions  are  originally  evolved  out 
of  the  more  complex  into  the  more  simple,  and  that  the  prog- 
ress of  science  is  nothing  more  than  a  progressive  unfolding 
into  distinct  consciousness  of  the  various  elements  compre- 
hended in  the  characters,  originally  known  to  us  in  their 
vague  or  confused  totality." 


CHAPTER  VI. 

THE   PRODUCTS   OF  THOUGHT. III.  REASONINGS. 

§  55.  The  Third  gradation  of  Thought  is  the  Reasoning. 
Like  the  Concept,  it  is  derived  from  the  Judgment.  Reasoning_ 
It  differs  from  the  Concept  in  its  form,  as,  unlike  what  l* is- 
that,  it  retains  the  full  forms  of  the  Judgment,  and  accord- 
ingly, also,  to  a  certain  extent,  it  differs  from  it  in  the  mode 
of  its  derivation.  It  differs  from  the  Judgment  proper  in 
this  respect,  that  it  is  a  derivation  from  a  Judgment  —  a 
traced  movement  of  Thought,  superadded  to  that  which  con- 
stitutes the  Judgment.  It  is  not  the  derived  Judgment,  not 
the  mere  terminus,  the  point  at  the  end  of  the  line  over  which 
the  Thought  has  moved,  hut  the  line  itself  as  traced  in  the 
movement  of  the  Thought.  When  viewed  as  a  resultant  prod- 
uct of  Thought,  therefore,  it  must  be  regarded  as  the  track 
of  Thought  left  marked  by  the  movement,  not  the  mere 
attained  object  or  goal  of  the  movement,  which  is  nothing 
more  than  a  Judgment.  We  are  carefully  to  distinguish, 
therefore,  a  Reasoning  from  the  Conclusion — from  the  Judg- 
ment which  is  attained  by  the  reasoning. 

A  Reasoning,  thus,  is  a  derivation  of  a  Judgment  from 
another  Judgment  or  Judgments. 

§  56.  The   term  Reasoning  is  ambiguously  employed  to 
denote  both  the  act,  and,  also,  the  product  of  the   „ 

1  Denomina- 

act.     In  its   different  gradations,  this  process    of  tions  of  the 

Dl"OCGSS 

Thought  has  obtained  a  variety  of  other  designa- 
tions, which  may  here  for  convenience  be  summarily  enumer- 
ated and  explained. 

"  Considered  as  an  act,  Reasoning,  or  Discourse  of  Reason 


92  PURE  LOGIC. 

(to  \oyt£eo~9ca,  AoyioyAos,  Siavoia,  to  Biavoelcrdai),  is,  likewise, 
called  the  act  or  process  of  Argumentation  (argumentationis), 
of  Ratiocination  (ratiocinationis,)  of  Inference  or  Illation 
(infer  endi),  of  Collecting  (colligendi),  of  Concluding  (con- 
cludendi),  of  Syllogizing  (tov  avWoyi&crOaL,  barbarously  syl- 
logisandi).  The  term  Reasoning  is  likewise  given  to  the 
product  of  the  act ;  and  a  reasoning  in  this  sense  (ratiocina- 
tio,  ratiociniwn)  is  likewise  called  an  Argumentation  (argu- 
mentatio)  ;  also,  frequently,  an  Argument  (argumentum),  an 
Inference  or  Illation  (illatio),  a  Collection  (collectio),  a  Con- 
clusion (conclusio,  o-u/A7repacr/x.a),  and,  finally,  a  Syllogism 
(avWoy  loyxos)  • 

"Reasoning  is  a  modification  from  the  French  raisonner 
whSi  the  (and  this  a  derivation  from  the  Latin  ratio),  and 
process  of       corresponds  to  ratiocination  which  has  indeed  been 

Reasoning  is  i 

denominated,  immediately  transferred  into  our  language  under 
the  form  of  ratiocination.     Ratiocination  denotes 

Reasoning. 

Ratiocina-  properly  the  process,  but  improperly,  also,  the 
product  of  reasoning ;  Ratiocinium  marks  exclu- 
sively the  product.  The  original  meaning  of  ratio  was 
computation,  and  from  the  calculation  of  numbers  it  was 
transferred  to  the  process  of  mediate  comparison  in  general. 

Discourse  (discursus,  8iai/oia)  indicates  the  opera- 
Discourse.  P  A,  ,      ,         ,    ]  n 

tion  ot  comparison,  the  running  backward  and  lor- 

ward  between  the  characters  or  notes  of  objects  (discurrero 
inter  notas,  SuwoeZcr&u).  The  terms  discotirse  and  discursus, 
Siavoia,  are,  however,  often  used  for  the  reasoning  process, 
strictly  considered,  and  discursive  is  even  applied  to  denote 
mediate,  in  opposition  to  intuitive,  judgment,  as  is  done  by 
Milton.  The  compound  term,  discourse  of  reason,  unambig- 
uously marks  its  employment  in  this  sense.    Arqu- 

Argumenta-  J  .  ,     r     J  . 

tion.  Argu-  mentation  is  derived  from  argumentari,  which 
means  argumentis  uti ;  argument  again,  argu- 
mentum —  what  is  assumed  in  order  to  argue  something  — 
is  properly  the  middle  notion  in  a  reasoning  —  that  through 
which  the  conclusion  is  established ;  and  by  the  Latin  Rhet- 


REASONINGS.  93 

oricians  it  was  defined,  '  probabile  inventum  ad  faciendam 
fdem.'      It  is  often,  however,  applied  as  coextensive  with 
argumentation.      Inference  or  Illation  (from  in- 
fero)  indicates  the  carrying  out  into  the  last  prop- 
osition what   was   virtually   contained    in    the    antecedent 
judgments.       To    conclude    (concludere) ,   again, 
signifies  the  act  of  connecting  and  shutting  into     oconcu  e 
the  last  proposition  the  two  notions  which  stood  apart  in  the 
two   first.      A  conclusion   (conclusio)    is  usually 

.    ,  .      .  .  .„        .  Conclusion. 

taken,  in  its  strict  or  proper  signification,  to  mean 
the  last  proposition   of  a  reasoning ;  it  is,  sometimes,  how- 
ever, used  to  express  the  product  of  the  whole  process.     To 
syllogize   means   to  form   syllogisms.      Syllogism  To  s  ll0  . 
(o-uXAoyio-fids)  seems  originally,  like  ratio,  to  have   Syllogism. 
denoted  a  computation  —  an  adding  up  ;  and,  like  the  greater 
part  of  the  technical  terms  of  Logic  in  general,  was  borrowed 
by  Aristotle  from  the  mathematicians.      ^vAAoyicr/Aos  may, 
however,  be  considered  as  expressing  only  what  the  compo- 
sition of  the  word  denotes  —  a  collecting  together  ;  for  crvAAo- 
yi£e<T0(H  comes  from    o-vXXeyeiv,  which  signifies   to   collect. 
Finally,  in  Latin,  a  syllogism  is  called  collectio, 
and  to  reason,  colligere.     This  refers  to  the  act  of 
collecting,  in  the  conclusion,  the  two  notions  scattered  in  the 
premises." 

§  57.  A  Reasoning  is  composed  of  two  parts  —  the  origi- 
nal Judgment  or  Judgments  which  are  the  original   integrant 
datum  in  the  process,  and  the  movement  of  the  Reasoning. 
Thought  in  the  process.     As  the   datum   is   re-  anions11* 
garded  as  logically  determining  and  preceding,  it  quent- 
is  called  the  Antecedent,  and  the  other  part,  regarded  as  logi- 
cally determined,  or  following,  is  called  the   Consequent.     Its 
proper  sign  is  therefore.     These  are  the  parts  of  a  Reason- 
ing regarded  as  an  Integrate  Whole. 

§  58.  The  Antecedent  in  a  Reasoning  may  consist  of  a 
single  Judgment,  or  of  a  plurality  of  Judgments.  DiVjSi0ns  °f 
If  it  consist  of  but  one  Judgment,  the  Reasoning  f^^fe-5 
is  called  an  Immediate  Reasoning.     If  the  ante-  Mediate- 


94  PURE  LOGIC. 

cedent  consists  of  more  than  one  Judgment,  the  Reasoning 
is  called  a  Mediate  Reasoning,  or,  more  technically,  a  Syllo- 
gism. 

Again,  in  a  Mediate  Reasoning,  the  Antecedent  may  con- 

Syiiooism-  s^  °f  *w0»  or  °f  more  tnan  two,  Judgments.  In 
Sorites.  the  former  case  there  emerges  the   Single  Syllo- 

gism ;  in  the  latter,  the  Polysyllogism,  also  called-the  Sorites. 

Still  further,  in  a  Mediate  Reasoning  the  derived  Judg- 
Cat  rfcai-  ment  may  be  mediated  through  the  relations  of 
Conditional.  the  terms  contained  in  the  Antecedent,  or  through 
those  of  the  copulas  —  that  is,  the  reasoning  may  turn  on 
proper  Concepts  as  wholes  and  parts  in  relations  to  each  other, 
or  on  proper  Judgments.  In  the  former  case,  there  emerges 
the  Categorical  Syllogism ;  in  the  latter  case,  the  so-called 
Conditional  Syllogism. 

Once  more,  the  reasoning  may  be  fully  expressed  in  the 
complete  regular  form  of  the  Syllogism,  or  may 

Enthymeme.  ...  -  J 

be  Elliptical,  one  or  other  of  the  several  Judg- 
ments which  form  it  being  suppressed  and  only  implied.  A 
reasoning  in  which  one  of  the  Judgments  is  thus  suppressed, 
is  called  an  Enthymeme.  This  is  the  more  common  form  of 
a  reasoning  in  actual  discourse.  Accordingly,  Aristotle  tells 
us  that  the  Enthymeme  is  the  Rhetorical  Syllogism. 

An  apparent  relaxation  of  logical  strictness  characterizes 
this  general  division  of  Reasonings.  It  arises  from  the  desire 
to  retain  the  familiar  nomenclature,  while  avoiding  the  error 
and  confusion  which  attend  it.  Logicians  have  generally 
represented  the  Hypothetical  and  Disjunctive  Syllogisms  as 
differing  from  the  Categorical  in  another  respect  than  that 
here  recognized.  And  this  treatment  has  necessarily  ob- 
scured and  complicated  the  exposition  of  the  proper  charac- 
ters of  the  several  species.  No  real  difficulty  will,  however, 
follow  our  continuing  the  old  denominations  ;  but  certain  ex- 
planations of  the  names  will  differ  from  those  to  be  found  in 
previous  logical  treatises. 

§  59.  An  Immediate  Reasoning  is  an  immediate  deri- 


REASONINGS.  95 

vation  of  a  Judgment  from  another  single  Judg-  j,^^.^ 
ment ;  as,  Man  is  rational  animal ;  therefore,  Man  Reasonings. 
is  rational. 

The  occasions  and  objects  of  our  thinking  often  demand 
that  the  form  of  an  attained  Judgment  be  changed,  so  that, 
the  primitive  Judgment  shall  be  treated  as  a  datum,  or  matter 
of  Thought,  yet  matter  having  characters  as  a  product  of 
Thought  that  may  be  recognized  as  of  its  own  originating, 
and  therefore  legitimate  and  valid  for  its  further  uses.  It 
becomes  important,  therefore,  to  determine  precisely  the 
allowed  limits  and  conditions  of  such  transformation,  so  that 
the  new  Judgment  must  be  recognized  as  valid.  It  will  be 
expedient  to  recall  here  some  of  the  fundamental  principles 
and  characters  of  Thought  as  already  ascertained  and  ex- 
pounded. 

All  Thought,  then,  proceeds  under  the  relation  of  Identity. 
It  is  valid  only  as  the  principle  of  the  Same  and  the  Differ- 
ent—  the  Identical  and  the  Non-identical  validates  it. 

Moreover,  as  Thought  is  an  activity  continuing  through 
time,  as  it  moves  on  over  the  Same,  the  principle  of  repeti- 
tion necessarily  comes  in,  and,  under  the  form  of  Synthesis, 
or  its  opposite,  Analysis,  exerts  its  sway  over  the  movements 
of  Thought.  All  valid  Thought,  accordingly,  is  under  the 
relations  of  Quantity  —  of  Whole  and  Parts,  so  that  where- 
soever these  relations  are  given  to  Thought  in  any  object  or 
matter,  Thought  may  move,  and  can  move  only  when  they 
are  thus  given.  Quantity,  in  fact,  is  but  identity  identified 
—  the  result  of  repeated  identifications. 

Further,  the  only  essential  relationships  in  Quantity  are 
the  two  relationships  :  (1)  of  Whole  to  Part,  with  its  recip- 
rocal of  Part  to  Whole  ;  and,  (2)  of  Part  to  Part.  All 
Thought  must,  to  be  valid  or  legitimate,  proceed  in  one  of 
these  two  relationships,  in  their  positive  or  their  negative 
forms  ;  and  all  thought  that  is  in  these  relations  is  so  far 
valid  - —  in  other  words,  bears  the  character  of  necessary 
truth. 


96  PURE  LOGIC. 

All  relations,  other  than  these  two  relations  of  Quantity  — 
those  of  Whole  to  Part,  and  of  Part  to  Part  —  are  foreign  to 
Thought ;  they  are  without  its  proper  characters,  the  charac- 
ters of  necessary  truth,  and  are  termed,  in  distinction,  Prob- 
lematic, Contingent,  Probable,  Possible,  according  to  the 
various  degrees  or  kinds  of  modality.  Hence  the  necessity 
of  keeping  in  mind  clearly  the  boundaries  between  the  mere 
datum,  or  matter  of  Thought,  and  Thought  itself.  Only  so 
far  as  we  intelligently  observe  this  distinction,  can  we  accept 
any  result  in  our  thought  as  necessarily  valid. 

Once  more,  the  data,  the  objects  of  Thought,  are  greatly 
diversified.  The  applications  of  Thought,  therefore,  to  attain 
the  objects  of  our  thinking,  must  accept  these  diversities  in 
the  essential  qualities  of  its  matter.  It  can  do  this,  however, 
only  within  the  limitations  of  its  own  proper  sphere  ;  only, 
therefore,  under  the  limitations  of  Quantity.  It  may,  thus, 
assume  the  different  kinds  of  Whole  that  are  given  to  it, 
which,  as  we  have  seen,  are  the  Integral,  the  Substantial, 
and  the  Causal ;  and  in  order  to  any  trustworthy  results  in 
the  interest  of  truth,  it  must  be  able  to  discriminate  these 
different  kinds  of  Whole,  and  thus  avoid  confounding  them 
in  its  movements. 

This  recapitulation  of  the  principles  of  Thought  will  guide 
us  in  the  enumeration  of  the  changes  possible  by  thought  in 
a  given  Judgment,  that  shall  be  legitimate  changes,  and  so 
bear  the  characters  of  necessary  truth. 

§  60.  The  first  kind  of  Immediate  Reasonings  is  that  of 

Conversion,  in  which  the  terms  of   the  original 

Judgment,  its  Subject  and  Predicate,  are  simply 

transposed.    Its  formula  is  :  A  =  B;  therefore,  B=  A.    The 

primitive  Judgment   is   called  the  Convertend ;  the  derived 

Judgment,  the  Converse. 

The  validity  of  this  Reasoning  is  too  obvious  .to  require 
extended  proof  or  illustration.  It  has  been  already  observed 
that  it  is  not  Thought  itself,  but  the  occasion  or  the  design  of 
Thought,  which  determines  which  of  the  two  objects  presented 


REASONINGS.  97 

to  it  shall  be  viewed  as  subject  and  which  as  predicate. 
Thought  itself  only  identifies  the  two.  It  is,  consequently, 
indifferent  to  Thought  which  of  the  two  be  the  occasion  or 
starting  point.  The  conversion  of  a  Judgment  cannot,  ac- 
cordingly, in  any  way  affect  its  validity. 

Tlje  Law  of  Identity,  which  presides  over  every  movement 
of  Thought,  here  prescribes  that  there  be  no  change  in  the 
quality  of  the  Judgment,  and  none  in  the  kind  of  Whole,  that 
is,  in  the  quantity  of  either  term.  The  specification  of  the 
diverse  applications  of  this  Law  in  the  conversion  of  a  Judg- 
ment, with  the  indications  of  the  necessity  for  a  peculiarly 
careful  attention  to  it  in  certain  cases,  will  properly  come 
under  consideration  in  the  Second  Part  of  Logical  science  — 
the  Doctrine  of  Methodology. 

§  61.  The  second  kind  of  Immediate  Reasonings  is  that  by 
Quantitative  Restriction,  in  which  one  or  both  of  Quantitative 
the  terms,  regarded  as  whole-,  are  changed  to  a  Restriction, 
logical  part  or  parts.  Its  formula  is  :  A  is  B,  therefore  some 
A  is  B.  The  primitive  Judgment  is  called  the  Restringend  ; 
the  derived  Judgment,  the  Restricted. 

The  logical  validity  of  this  form  of  Immediate  Reasoning 
is  equally  obvious  as  that  of  the  first  kind  by  Conversion. 
Every  whole  is  made  up  of  like  parts,  each  one  of  which 
may  be  recognized  as  identical,  in  some  respect,  with  any 
other  coordinate  part.  If  the  whole,  therefore,  is  identified 
with  another  whole,  any  part  may  be  identified  with  any  like 
part  of  the  second  whole. 

If  the  Restriction  is  confined  to  but  one  of  the  terms, 
either  the  Subject  or  the  Predicate,  it  is  called  Unilateral; 
if  extended  to  both  terms,  it  is  called  Bilateral. 

Examples  of  trilateral  Restriction  in  Quantity  are  — 

1.  Of  Subject:  Man  is  rational  animal ;  therefore,  Soc- 
rates is  rational  animal. 

2.  Of  Predicate  :  Man  is  rational  animal ;  therefore,  man 
is  rational. 

7 


98  PURE  LOGIC. 

Of  Bilateral:  Man  is  rational  animal ;  therefore,  Socrates 
is  rational. 

The  Law  that  governs  in  this  movement  of  Thought,  is 
that  of  Identity  as  applied  to  the  relation  of  Part  to  Whole. 
What  is  true  of  the  Whole  distributively  is  true  of  every 
part. 

§  62.  The  third  kind  of  Immediate  Reasonings  is  that  by 
Modal  Re-  Modal  Restriction,  in  which  the  modal  energy  of 
striction.  the  Judgment  is  reduced;  as,  A  must  he  B; 
therefore,  A  is  B. 

Nothing  need  be  said  to  illustrate  the  validity  of  this  proc- 
ess of  Thought.  We  have  distinguished  two  kinds  of  Modi- 
fied Judgment,  —  the  Necessary,  where  the  ground  of  the 
Judgment  is  given  as  lying  in  the  Thought  itself;  and  the 
Problematic,  where  the  ground  of  the  Judgment  lies  out  of 
the  proper  sphere  of  Thought.  The  other  kind  of  Judgment 
given  by  this  distinction  is,  of  course,  the  unmodified,  or  the 
simple  Assertory.  Now  it  is  plain  that  the  Necessary  must 
always  involve  both  the  Problematic  and  the  Assertory,  in- 
asmuch as  if  Thought  has  once  identified,  its  identification 
being  absolute  and  sovereign  throughout  the  realms  of 
Thought,  the  terms  it  has  once  identified  in  a  necessary 
Judgment  are  ever  and  everywhere,  whether  simply  or 
problematically,  identified  ;  as,  3  -}-  1  =  4  being  a  necessary 
Judgment,  these  terms  may  with  absolute  validity  be  ac- 
cepted as  identical  in  any  matter  foreign  to  Thought — any 
contingent  matter. 

The  governing  Law  in  this  process  of  Thought  is,  as  in 
the  last  enumerated,  that  of  Identity  as  applied  to  the  rela- 
tion of  Part  to  Whole.  Here  the  whole  is  one  of  Degree  or 
Intensity,  as  it  lies  in  the  judging  act,  not  in  the  matter 
judged.     The  stronger  ever  includes  the  weaker. 

§  63.  The  fourth  kind  of  Immediate  Reasonings  is  by 
Transfer-  Transference,  in  which  some  character  of  the 
ence.  Thought  in  the  copula  is  transferred  to  the  mat- 

ter in  the  terms ;  as,  A  is  not  B ;  therefore,  A  is  non-B. 


REASONINGS.  99 

This  process  of  Thought,  although  generally  recognized  by 
logicians  as  of  unquestioned  validity,  evidently  lacks  the 
character  of  perfectly  pure  Thought.  It  is  not  necessarily 
valid,  because  it  accepts  the  intermingling  of  Thought  with  its 
matter  as  legitimate,  whereas  to  confound  the  qualities  of  the 
thought  with  those  of  its  matter  is  precisely  the  grand  source 
of  error  against  which  the  Science  of  Logic  chiefly  seeks  to 
guard.  That  such  a  transference  is  not  of  itself  legitimate 
will  be  apparent  from  a  single  example.  Substitute  in  the 
formula  given,  for  A,  a  stone,  and  for  B,  vertebrate  ;  we  shall 
then  have  the  reasoning :  A  stone  is  not  vertebrate  ;  therefore, 
it  is  non-vertebrate  ;  that  is,  invertebrate.  It  is  obvious  that, 
in  the  transference,  we  have  changed  the  Thought  from  being 
purely  negative  in  its  quality  to  one  having  something  of  a 
positive  character.  Our  conclusion  is  a  palpable  falsity,  as 
we  have  ranked  a  stone  among  the  class  of  invertebrates. 
We  must  not  at  once  conclude  that  this  process  is  wholly 
extra-logical.  It  is  assuredly  a  process  of  Thought ;  and 
nothing  that  concerns  Thought  can  be  regarded  as  extra- 
logical.  It  is  the  part  of  logic  to  separate  the  element  of 
pure  Thought  from  the  hybrid  process,  and  so  indicate  pre- 
cisely what  there  is  of  logical  validity  in  it.  Certainly  there 
is  a  semblance  of  legitimacy  in  the  process,  else  logicians 
would  not  so  universally  have  accepted  it  without  question, 
for  we  find  it  thus  accepted  by  logical  purists  of  the  first 
degree,  who  have  insisted  upon  exterminating  from  the  science 
every  weed  of  matter,  and  upon  keeping  the  field  entirely 
free  to  the  purest  forms  of  Thought.  It  will  not  be  difficult 
to  discriminate  the  matter  from  the  form  here,  and  thus  to 
attain  the  proper  criteria  for  the  validity  of  such  a  process 
in  our  thinking. 

We  have  found  the  relations  of  Whole  and  Parts  to  be  the 
proper  relations  of  Thought.  Any  procedure  under  these  re- 
lations is  a  legitimate  and  valid  procedure  of  pure  Thought. 
If,  consequently,  any  matter  given  to  Thought  be  given  in 
these  relations,  then  Thought  can  move  on  in  necessary  cer- 


100  PURE  LOGIC. 

tainty  as  pure  Thought.  So  far,  then,  as  the  transfer  of  a 
quality  of  the  copula  from  it  to  either  of  the  terms  i.s  within 
this  relation  of  Whole  and  Part,  it  is  valid.  Thus,  substitut- 
ing for  B,  in  the  example  given,  a  term  thought  as  a  Whole, 
of  which  vertebrate  and  invertebrate  are  logically  Complement- 
ary Parts,  and  for  A,  a  term  given  as  a  part  of  that  Whole, 
say  butterfly,  then  the  transference  of  the  negative  becomes 
valid  —  we  can  conclude,  Butterfly  is  invertebrate.  We  have 
now  avoided  the  intermingling  of  thought  and  matter ;  the 
movement  has  been  within  the  proper  sphere  of  Thought ; 
from  the  proper  field  of  a  Judgment,  in  fact,  to  that  of  a  Con- 
cept. The  obvious  limitation  on  this  mode  of  reasoning,  thus, 
is  that  the  first  form  (B)  of  the  term  to  which  the  quality  of 
the  Judgment  is  transferred  be  recognized  as  a  part  comple- 
mentary of  the  second  form  (non-B),  and  that  the  other  term 
(A)  be  recognized  as  lesser  part  of  one  or  the  other  of  these 
complementary  pai'ts. 

The  logical  validity  of  the  Thought  as  thus  regulated  is 
obvious  on  the  principle  that  in  a  given  whole  any  one  part 
is  complementary  of  the  rest,  and  reciprocally  the  rest  is 
complementary  of  it ;  and  that  any  lower  part  of  that  whole 
must  belong  to  one  of  these  complementary  parts.  If,  thus, 
there  be  a  whole  C,  of  which  A  and  B  are  parts,  and  B  and 
non-B  are  the  two  complements  of  that  whole,  if  A  is  not  B, 
it  necessarily  is  non-B.  Otherwise ;  A  being  some  part  of 
C.  and  B  and  non-B  being  also  complementary  parts  of  C, 
if  A  is  not  B,  it  must  be  non-B. 

This  form  of  Immediate  Reasoning,  by  transference  of 
Quality  from  the  copula  to  one  of  the  terms,  is  legitimate 
in  each  species  of  Wholes.  Thus,  in  a  Spaeial  Whole,  if  by 
A  and  B  in  the  formula  given  be  understood  respectively 
halves  of  a  square  bisected  by  a  diagonal,  we  shall  have  : 
This  half — A  —  is  not  B;  therefore,  it  is  non-B. 

So  in  a  Substantial  Whole ;  if  rational  and  animal  be 
parts,  making  up  the  same  whole,  man  ;  then  if  (A)  animal 
is  not  (B)  rational,  it  is  {non-B)  non-rational ;  or  (A)  an- 


REASONINGS.  101 

imal  is  not   (B)   rational;  therefore,  (A)  animal  is  (non- 
B)  non-rational,  that  is,  irrational. 

In  the  same  way,  in  a  Causal  Whole,  if  a  magnet  be  viewed 
as  a  cause  acting,  the  parts  through  which  are  attraction  and 
repulsion  complementary  of  each  other,  so  that  magnet  in 
this  use  of  the  term,  as  a  cause  only,  attracts  or  repels,  then 
we  may  reason:  if  this  acting  magnet  does  not  attract,  then 
it  does  non-attract,  that  is,  repel ; —  non-attracting  being  here 
repelling,  or  the  necessary  alternative,  that  is,  the  comple- 
mentary part  of  attracting  in  an  acting  magnet. 

Reasonings  by  Transference  are  of  two  varieties.     1.  The 
proper  Quality  of  the  copula  may  be  transferred   Transfer- 
to  one  of  the  terms ;  as,  Mind  is  not  material ;   Qualitative ; 
therefore,  it  is  immaterial ;  Necessity  does  not  be-  2-  ModaL 
long  to  rational  being  ;  therefore,  non-necessity,  that  is,  Free- 
dom, belongs  to  rational  being. 

2.  The  Modality  of  the  copula  may  be  transferred  to  one 
of  the  terms*  as,  Bain  may  fall  to-morrow;  therefore,  Bain  is 
a  possible  event  to-morrow. 

The  exposition  given  so  far  of  this  form  of  Immediate 
Reasoning  has,  for  the  sake  of  clearness,  proceeded  in  forms 
of  illustration  appropriate  strictly  and  throughout  only  to  the 
first  of  these  varieties.  The  movement  of  Thought  we  found 
to  be  valid,  inasmuch  as  Thought  did  not  move  out  of  its  own 
sphere  —  kept  within  its  own  proper  relationships  of  Whole 
and  Part,  or  more  specifically  within  relations  of  Contradict- 
ory Disjunction.  It  is  equally  valid  in  the  second  variety, 
if  only  a  proper  modality  of  Thought  be  transferred.  If  the 
derived  Judgment  be  interpreted  as  under  a  modality  of 
Thought,  the  reasoning  is  obviously  not  universally,  that  is,  ne- 
cessarily, valid.  Thus,  in  regions  where  rain  is  only  in  one 
part  of  the  year,  although  a  stranger  ignorant  of  the  pecul- 
iarities of  the  climate  might  reason  with  himself,  so  far  as 
thought  can  go  :  Bain  may  fall  to-morrow  ;  therefore,  Bain 
is  a  possible  event  to-morrow,  it  would  be  a  false  conclusion, 
if  the  modal  word  possible  were  to  be  interpreted  as  expres- 


102  PURE  LOGIC. 

sive  of  physical  modality.  Only  so  far  as  proper  modality  of 
thought,  can  modality,  thus,  be  transferred  from  the  copula  to 
the  terms  —  from  the  thought  to  the  matter. 

In  order  to  effect  the  transference  legitimately,  it  may  be 
necessary  to  bring  into  the  antecedent  another  Judgment,  so 
that  we  shall  have  a  Mediate  Reasoning.  Thus,  in  the  first 
case,  we  may  need  to  add  for  a  logical  antecedent  to  the 
Judgment,  A  is  not  B,  the  Judgment,  A  is  part  of  B,  or  of 
non-B.     Then  the  conclusion  is  legitimated. 

§  64.  The  fifth  kind  of  Immediate  Reasoning  is  that  of 
Disjunction.  From  a  Disjunctive  Judgment  wc 
lsjur  on.  may  immediately  infer  both,  (1.)  That  the  dis- 
junct members  are  not  the  same  ;  and,  (2.)  That  the  one  is 
contradictory  of  the  other.  Thus  from  A  is  either  B  or  G, 
we  may  immediately  infer  either,  (1.)  That  B  is  not  G  ;  or, 
(2.)  That  non-B  is  G.  Or  Angles  are  right,  acute,  or  obtuse  ; 
therefore,  (1.)  Right  angles  are  neither  acute  nor  obtuse ; 
and,  (2.)   No  acute  angle  is  either  right  or  obtuse. 

The  validity  of  this  reasoning  is  evident  from  the  nature 
of  Disjunction,  which  is  the  principle  of  the  relation  of  Part 
and  Complementary  Part. 

§  65.  The  sixth  kind  of  Immediate  Reasoning  is  that  of 
Composition,  in  which,   from  several   Judgments 

Composition.  J  /  .  ° 

with  the  same  term  either  as  subject  or  predicate, 
a  Judgment  may  be  derived  in  which,  with  this  term  remain- 
ing, the  other  term  shall  be  the  sum  of  the  other  terms. 
Thus,  if  A  is  B,  and  G  is  B,  then  A-\-G  is  B  ;  or,  If  animals 
are  organic  and  vegetables  are  organic,  then  animals  and 
vegetables,  that  is,  all  living  beings,  are  organic.  If  all  body 
has  length,  and  all  body  has  breadth,  and  all  body  has  depth  ; 
then  all  body  has  length,  breadth,  and  depth,  that  is,  is  solid. 

The  principle  of  this  kind  of  Immediate  Reasoning  is  ob- 
viously that  of  the  Concept.  No  further  illustration  of  its 
nature  or  validity  is  necessary. 

§  66.  Mediate  Reasonings  we  have  distinguished  into  two 
Cate  oricai  cla3ses>  according  as  they  embrace  or  not  new 
Syllogism.       matter  not  in  the  primitive  Judgment.     Those  of 


REASONINGS.  103 

the  first  class  in  which  new  matter  is  introduced,  if  the  new 
matter  be  in  a  single  term  of  a  single  new  Judgment,  are 
called  Categorical  Syllogisms.  "We  thus  have  the  following 
definition  :  — 

A  Single  Categorical  Syllogism  is  one  whose  ante- 
cedent member  contains  two  Judgments,  to  which   Its  Defini_ 
but  one  term  in  each  is  common,  the  other  being   tl0n- 
different ;  as,  Man  is  mortal ;   Caius  is  a  man  ;  therefore, 
Caius  is  mortal. 

In  this  example,  the  first  Judgment  in  the  antecedent 
member  of  the  Reasoning  contains  for  its  matter  the  terms 
man  and  mortal ;  the  second  Judgment  contains,  hesides  the 
term  man  in  the  first,  new  matter  in  the  term  Caius. 

The  nature  of  this  movement  of  Thought  it  will  not  be 
difficult  to  render  intelligible.  A  primitive  condition  of 
Thought  we  have  found  to  be  a  Law  imposing  upon  it,  if  it 
move  at  all,  the  necessity  of  recognizing  the  identity  or  the 
non-identity  of  any  two  objects  presented  to  it.  Now  as  the 
essential  quality  of  Intelligence  is  clearness,  it  may  be  im- 
possible for  Thought  to  move  at  all,  to  recognize  identity  or 
non-identity,  that  is,  affirm  sameness  or  difference,  for  want 
of  light.  It  necessarily,  therefore,  remains  in  doubt.  A  new 
cognition  in  the  form  of  another  Judgment  may  afford  the 
requisite  light,  and  enable  the  Thought  to  move  from  the 
state  of  doubt  to  that  of  a  determinate  Judgment. 

This  new  enlightening  Judgment,  however,  must  stand  in 
a  certain  definite  relation  to  the  two  terms  that  were  origin- 
ally presented  to  be  identified  or  differenced  ;  and  this  rela- 
tion must  be  one  that  lies  within  the  sphere  of  Thought ;  — 
must  be,  in  other  words,  a  relation  of  Quantity  —  of  Whole 
to  Part,  or  of  Part  to  Part.  If  the  two  original  terms,  say 
A  and  C,  were,  one  of  them,  A,  a  whole  of  which  another 
term  B  were  a  part,  and  B  also  were  a  whole  of  which  C 
were  a  part,  then  Thought  could  at  once  move  in  its  own 
sphere  of  Quantity  and  recognize  C,  inasmuch  as  it  is  a  part 
of  B}  as  also  a  part  of  A  of  which  B  is  a  part ;  in  other  words 


104  PURE  LOGIC. 

conclude  that,  if  C  is  a  part  of  B,  and  B  is  a  part  of  A,  C  is 
a  part  of  A.  This  may  perhaps  be  better  illustrated  in  a 
concrete  example.  We  may  have  the  two  objects  of  thought 
given  to  us,  of  sponge  and  animal ;  and  may  be  unable  for 
want  of  light  to  recognize  any  identity  between  them  so  as  to 
be  warranted  in  affirming  that  the  sponge  is  an  animal,  or  in 
affirming  that  a  sponge  is  not  an  animal —  we  stand  in  doubt. 
But  by  the  aid  of  new  Judgments,  as  that  the  sponge  is  sen- 
tient, and  that  all  sentient  beings  are  animal,  this  doubt  is  re- 
moved, as  we  recognize  that,  the  sponge  being  a  part  of 
sentient  beings  and  sentient  beings  a  part  of  animal,  the 
sponge  must  be  part  also  of  animal  —  that  sponge  is  identical 
with  part  of  animal. 

This  illustration  characterizes  but  one  of  the  two  great 
classes  of  Mediate  Reasonings —  the  so-called  Deductive 
Reasonings  or  Syllogisms.  Logicians  have  generally  limited 
their  view  to  this  species,  giving  but  incidental  consideration 
to  the  other.  Indeed,  many,  like  Dr.  Whately,  have  endeav- 
ored to  subordinate  all  forms  of  Reasoning  to  the  Deductive 
Syllogism,  and  with  him  the  terms  Reasoning  and  Syllogism 
are  convertible.  Sir  William  Hamilton  has  exposed  the 
error  of  those  views,  but  has  failed  to  elaborate  any  trust- 
worthy scheme  that  should  comprehend  all  reasoning.  In- 
deed, he  seems  to  have  utterly  overlooked  one  of  the  two  fun- 
damental relationships  in  Thought.  While  recognizing  all 
Thought  as  necessarily  proceeding  in  the  relations  of  Quan- 
tity, he  has  seemed  to  regard  but  one  specific  relation  among 
them,  viz:  that  between  the  Whole  and  Part;  or,  more  exactly, 
perhaps,  he  makes  of  this  single  relation  two  —  that  from  the 
Whole  to  the  Part,  and  the  converse,  from  the  Part  to  the 
Whole,  forgetting  that  these  two  supposed  relations  are 
necessarily  one  in  Thought,  the  movement  being  indifferent 
so  far  as  Thought  is  concerned,  in  the  one  direction  or  in  the 
other,  and  that  it  is  the  object  or  proposed  aim  in  thinking, 
the  occasion  external  to  the  thought,  that  determines  the 
direction  of  the  movement,  whether  from  this  goal  or  from 


REASONINGS.  105 

that,  from  the  Whole  or  from  the  Part.  The  relationship 
between  the  Whole  and  the  Part,  thus,  is  the  same,  whether 
we  think  that  the  Whole  contains  the  Part,  or  that  the  Part 
is  contained  in  the  Whole  ;  and  the  distinction  of  Hamilton  is 
fallacious  or  utterly  futile.  But  there  is  another  entirely  dis- 
tinguishable relation  of  Quantity  —  that  of  Part  to  Part. 
Only  as  we  admit  this  relation  between  part  and  complement- 
ary part  in  every  whole,  can  we  admit  any  disjunction  in 
Thought  —  any  recognition  of  Same  and  Different.  The  very 
notion  of  Difference  implies  a  necessary  relationship  between 
Parts.  This  relation  between  Part  and  Complementary  part, 
given  at  once  and  necessarily  with  the  relation  of  Whole  and 
Part,  permeates  Thought  everywhere  as  its  validating  con- 
dition. 

§  67.  Categorical  Syllogisms  are  divided  into  two  classes 
in  respect  of  the  two  different  directions  in  which  Thought 
may  move.  If  the  movement  be  between  the  two  relatives 
of  Quantity,  Whole  and  Part,  the  Syllogism  is  called  De- 
ductive. If,  on  the  other  hand,  the  movement  of  Thought 
be  between  relative  Part  and  Part,  the  Syllogism  is  called 
Inductive.  A  Syllogism  of  either  class  may  alike  proceed 
either  in  Comprehensive  or  in  Extensive  Quantity. 

§  68.  A  Deductive  Syllogism  is  a  Mediate  Reasoning 
in  which  the  movement  of  Thought  is  from  a  Whole  to  a 
Part,  mediated  through  a  middle  term,  which  is,  respectively, 
a  part  of  that  whole  and  a  whole  of  that  part ;  as,  Man  is 
mortal;   Cains  is  a  man;  therefore,  Caius  is  mortal. 

As  the  Deductive  Syllogism  is  a  Mediate  Reasoning,  its 
datum  must  consist  of  two  Judgments,  which,  as  given  to 
Thought,  are  not  of  course  at  all  validated  by  the  Reasoning. 
They  must  be  regarded  consequently  as  only  assumed  for 
the  Reasoning,  or  must  rest  on  evidence,  foreign  to  it.  But 
the  movement  of  Thought  in  itself  may  be  valid,  although 
the  given  Judgments  are  false;  just  as  an  arithmetical  proc- 
ess may  be  correct,  although  applied  to  unreal  objects. 

These  two  given  Judgments  constitute  the  Antecedent ;  as 


106  PURE  LOGIC. 

the  derived  Judgment  is  the  Consequent  of  the  Reasoning. 
From  their  naturally  preceding  the  Consequent,  they  are 
called  the  Premises  (Proposiliones  prcemissce). 

As  might  be  supposed,  not  any  two  Judgments  taken  for- 
tuitously can  be  accepted  as  premises  in  the  same  Reasoning. 
In  the  first  place,  both  of  the  Judgments  must  contain  the 
same  term  in  common,  the  other  term  in  each  being  different. 
In  the  next  place,  this  term  that  is  common  to  the  two  Judg- 
ments, must  be  a  part  in  relation  to  the  remaining  term  in 
one  Judgment,  and,  also,  a  whole  in  relation  to  the  remain- 
ing term  in  the  other  Judgment.  Thus,  in  the  example 
given,  the  term  man  is  a  part  of  the  class  mortal,  but  a  whole 
class  of  which  Caius  is  part.  From  its  bearing  this  two- 
fold relation  to  the  remaining  terms  in  the  premises,  of  part 
to  one,  and  of  whole  to  the  other,  this  common  term  is  called 
the  Middle  Term  ;  and  the  other  terms  are  called  the  Ex- 
tremes (extrema,  a.Kpa).  When  this  relation  exists,  and  only 
then,  can  two  judgments  be  accepted  as  premises ;  and,  to 
use  the  expression  of  Aristotle,  "  when  the  three  terms  are 
so  related  to  one  another  that  the  last  is  in  the  middle  as  a 
whole,  and  the  middle  is  or  is  not  in  the  first  as  a  whole,  a 
perfect  syllogism  necessarily  emerges." 

Of  the  Extremes,  that  which  as  a  whole  contains  the 
Middle  Term  is  called  the  Major  Term  ;  and  that  which  is 
contained  in  or  under  the  Middle,  is  called  the  Minor  Term. 

A  convenient  mode  of  designating  the  Terms  is  by  the  use 
of  the  letters  W,  P,  and  M :  W  denoting  the  Major  Term ; 
P,  the  Minor;  and  M,  the  Middle. 

The  very  nature  of  the  process  excludes  the  possibility  of 
there  being  more  than  these  three  terms  in  a  single.  Deduc- 
tive Reasoning  —  the  two  Extremes  being  compared  through 
the  Middle  Term.  A  Term,  it  must  be  recollected,  may  con- 
sist of  several  words  ;  they  must,  however,  constitute  one 
object  of  thought,  and  so  be  capable  of  being  used  as  a  sub- 
ject or  as  a  predicate.  On  the  other  hand,  if  a  single  word  be 
used  in  different  meanings  in  the  several  propositions  which 


REASONINGS.  107 

compose  the  Syllogism,  we  have,  under  the  guise  of  three, 
in  reality  more  than  three,  terms.  This  is  the  nature  of  the 
fallacy  of  four  terms,  quaternio  terminorum.  As  in  the  Syl- 
logism : 

Animals  are  void  of  reason  ; 

Man  is  an  animal ; 

Therefore,  man  is  void  of  reason. 

Here  the  middle  term,  animal,  is  used  in  the  Major  pre- 
mise as  synonymous  with  brute,  a  conspecies  of  man,  and  so 
excluding  it.  In  the  Minor  premise  it  is  used  to  denote  a 
genus  containing  under  it  the  two  species,  rational  and  irra- 
tional; —  as,  in  other  words,  including  man.  There  are, 
thus,  really  two  different  objects  of  thought,  two  logical  terms 
presented  in  the  two  premises  by  the  same  word  —  animal. 

In  respect  of  the  Propositions,  it  is  equally  clear  that  there 
must  be  one  showing  the  relation  between  the  Major  term  and 
the  Middle  term  —  a  proper  Sumption  ;  that  there  must  be 
another  showing  the  relation  between  the  Middle  and  the 
Minor  —  a  proper  Subsumption  ;  and,  moreover,  a  Conclu- 
sion, showing  the  relation  between  the  Major  and  the  Minor. 

The  Hindoo  system  seems  to  have  recognized  five  propo- 
sitions, called  the  Assertion,  the  Reason,  the  Proposition,  the 
Assumption,  and  the  Deduction  in  a  Reasoning  :  as  "  1.  The 
mountain  has  fire  ;  2.  For  it  has  smoke  ;  3.  But  all  that  has 
smoke  has  fire  ;  4.  And  the  mountain  has  smoke  ;  5.  There- 
fore, the  mountain  has  fire."  But  it  is  apparent  that  the  first 
proposition,  which  is  called  the  Assertion,  is  the  same  as  the 
fifth,  the  Deduction  or  Conclusion  ;  and  the  second,  called  the 
Reason,  is  the  same  as  the  fourth,  called  the  Assumption. 
There  are,  in  fact,  only  three  propositions  entering  into  the 
Reasoning  proper.  The  premises  must  be  regarded  for  the 
Reasoning  as  assumed ;  they  are  the  data  to  Thought  in  its 
movement. 

Of  the  two  premises,  that  one  which  enounces  the  relation 
of  the  Major  term  to  the  Middle,  is  called  the  Major  Pre- 
mise, also  the  Sumption  (propositio  major,  sumptio  major, 


108  PURE  LOGIC. 

sumptio,  thesis).  The  other  of  the  premises  which  enounces 
the  relation  of  the  Minor  Term  to  the  Middle,  is  called  the 
Minor  Premise,  also  the  Subsumption  (propositi*}  minor,  as- 
sumptio,  subsumptum,  subsumptio,  sumptio  minor).  It  is  not, 
of  course,  the  order  in  which  the  premises  are  placed  in  the 
Syllogism  which  determines  the  one  to  he  the  Major,  the 
other  to  be  the  Minor  Premise.  The  order  is  merely  of  the 
form,  the  verbal  expression,  and  does  not  concern  the  thought. 
Which  shall  precede  is,  hence,  a  matter  of  indifference  so 
far  as  the  essential  character  of  the  reasoning  is  concerned. 

The  Consequent  is  the  derived  Judgment  —  the  result  or 
goal  of  the  Reasoning.  It  enounces  the  relation  of  the  Minor 
term  to  the  Major,  and  is  called  the  Conclusion  (conclusio, 
collectio,  crvfjui-ipaafia).  It  is  usually,  in  formal  and  fully 
stated  Syllogisms,  designated  by  the  Conjunction,  therefore, 
or  by  synonymous  expressions,  as  consequently,  and  the  like. 

Logicians,  recognizing  only  Extensive  Quantity,  and  having 
accepted  the  division  of  Propositions  into  the  four  kinds,  Uni- 
versal Affirmative,  Particular  Affirmative,  Universal  Nega- 
tive, and  Particular  Negative,  as  their  ruling  division,  have 
connected  the  consideration  of  Quantity  with  that  of  Quality 
in  their  formal  treatment  of  the  Syllogism.  It  has  been, 
accordingly,  prescribed  by  them  that  the  Sumption  must  be 
definite,  that  is,  universal  or  single,  while  the  Subsumption 
may  be  in  either  Quantity,  definite  or  indefinite.  But  this 
teaching  is  all  unnecessary,  and  tends  to  confuse  and  to  mis- 
lead. The  one  principle  is  that  each  term  must  in  each  sev- 
eral proposition  be  taken  in  the  same  meaning  in  respect  of 
Quantity,  as  well  as  in  respect  of  nature  of  object  denoted  by 
it.  If  the  Minor  term  be  restricted  by  any  limiting  word,  as 
some,  few,  or  the  like,  while  it  is  yet  recognized  in  the  Syllo- 
gism as  being  contained  unrestricted  in  the  Middle,  we  have, 
in  fact,  a  mixed  reasoning  —  a  proper  mediate  reasoning  com- 
bined with  an  immediate  reasoning  of  the  Restrictive  Class. 
It  is  clear  we  cannot  reason  :  Some  men  are  learned ;  Caius 
is  a  man  ;  therefore,  Caius  is  learned,  simply  because  the 


REASONINGS.  109 

Middle  term  in  the  Sumption  is  not  used  in  the  same  extent 
of  meaning  as  in  the  Subsumption.  There  are  really  four 
terms.  When  we  have  a  Subsumption  in  Particular  Quan- 
tity, so-called,  as,  for  example,  Man  is  mortal;  some  rational 
beings  are  men ;  obviously  we  cannot  conclude  :  therefore, 
rational  beings  are  mortal ;  for  we  have  changed  the  mean- 
ing of  the  Minor  term,  using  it  in  a  wider  extent  in  the  Con- 
clusion, and  a  narrower  in  the  Subsumption.  But  commonly, 
if  the  Minor  term  be  used  in  a  wider  extent  of  meaning  in 
the  Subsumption  than  in  the  Conclusion,  as,  Man  is  mortal  ; 
philosophers  are  men  ;  therefore,  some  philosophers  are  mortal, 
we  have  a  valid  conclusion,  it  is  true,  but  a  mixed  reasoning, 
as  just  stated. 

Logicians  have  enounced  the  comprehensive  rule  for  the 
conclusion,  thus :  The  Conclusion  must  always  follow  the 
weaker  or  worser  part,  the  negative  and  the  particular  being 
regarded  as  the  weaker  or  the  worser  in  respect  of  the  affirm- 
ative and  the  universal. 

The  general  relations  of  the  several  judgments  which  com- 
pose a  Deductive  Reasoning  to  one  another,  moreover,  logi- 
cians have  illustrated  to  the  eye  by  means  of  three  unequal 
circles,  the  largest  of  which  represents  the  Major  term,  the 
smallest  the  Minor,  and  the  intermediate  the  Middle  term. 
If  we  call  them  respectively  W,  P,  and  M,  then  it  will 
readily  be  seen  if  the  largest  circle,  W,  include  the  middle 
circle,  M,  and  if,  also,  M  include  the  least  circle,  P,  the 
largest  circle,  W,  must  include  the  least  circle,  P. 

§  69.  As  the  relation  of  Whole  and  Part  may  exist  in 
either  of  the  two  kinds  of  Logical  Quantity,  Ex- 

„  ,  .  .      .         ,     .  Two  kinds 

tension   or   Comprehension,  it  is  obvious  we  may   of  Deductive 
have  two  kinds  of  Deductive  Syllogism,  the  Ex-   SyUoglsm- 
tensive  and  the  Comprehensive  or  Intensive. 

In  the  Extensive  form,  the  Middle  is  said  to  be  contained 
under  the  Major  term,  and  to  contain  under  it  the   x  Extensive 
Minor  term.     In  the  Intensive  form,  the  Middle  is   2-  intensive. 
said  to  be  contained  in  the  Major  term,  and  to  contain  in  it 


110  PURE  LOGIC. 

the  Minor  term.  The  Syllogism,  as  ordinarily  expressed, 
may  be  explicated  in  either  Quantity.  Thus  in  the  Syllogism, 
Man  is  mortal ;  Caius  is  a  man  ;  therefore,  Caius  is  mortal, 
if  we  explicate  it  as  in  Extensive  Quantity,  we  shall  have  the 
following : 

The  Middle  term,  man,  is  contained  under  the  Major  term, 
mortal ;  that  is,  man  is  a  part  of  the  class  mortal: 

The  Minor  term,  Caius,  is  contained  under  the  Middle 
term,  man  ;  that  is,  Caius  is  a  part  of  the  class  man  : 

Therefore,  the  Minor  term,  Caius,  is  contained  under  the 
Major  term,  mortal;  that  is,  Caius  is  a  part  of  the  class  mortal. 

If,  again,  the  Syllogism  be  construed  as  in  Intensive  Quan- 
tity, the  explication  will  be  as  follows : 

The  Major  term,  Caius,  contains  in  it  the  Middle  Term, 
man  ;  that  is,  the  complement  of  attributes,  Caius,  contains 
in  it,  as  part,  the  complement  of  attributes,  man  : 

The  Middle  term,  man,  contains  in  it  the  Minor  term, 
mortal ;  that  is,  the  attribute,  man,  contains  in  it,  as  part,  the 
attribute  mortal  : 

Therefore,  the  Major  term,  Caius,  contains  in  it  the  Minor 
term,  mortal ;  that  is,  the  complement  of  attributes,  Caius, 
contains  in  it  as  part  the  attribute  mortal. 

It  will  be  noticed  that  the  term  man  is  the  Middle  term  in 
each  explication  ;  but  the  two  other  terms  change  places  ;  — 
the  Major  term  in  the  Extensive  form  becoming  the  Minor 
in  the  Intensive ;  and  the  Minor  in  the  former  becoming  the 
Major  in  the  latter.  Accordingly,  the  Major  premise,  which 
in  the  Extensive  form  compares  the  Major  term,  mortal,  with 
the  Middle  term,  man,  in  the  Intensive  form  compares  Caius, 
as  the  Major  term,  with  the  Middle ;  and  a  corresponding 
change  takes  place  in  the  Minor  premise.  In  other  words, 
the  Premises  change  with  the  changed  relations  of  the  Ex- 
tremes to  the  Middle  term. 

It  will  also  be  seen  that  the  one  may  easily  be  converted 
into  the  other  without  affecting  the  validity  of  the  reasoning. 
But  the  formula  W  contains  M ;  M  contains  P ;  therefore, 


REASONINGS.  HI 

W contains  P,  is  the  one  universal  formula  for  all  Affirma- 
tive Categorical  Syllogisms  in  either  quantity.  This,  how- 
ever, may  be  stated  in  the  passive  form,  but  then  preposi- 
tions come  into  use,  and  the  kind  of  quantity  is  at  once  indi- 
cated by  them.  Thus,  in  Extensive  Quantity,  it  would  be 
expressed  :  M  is  contained  under  W ;  P  is  contained  under 
M ;  therefore,  P  is  contained  under  W.  While,  in  Intensive 
Quantity,  we  should  have  :  Mis  contained  in  W ;  P  is  con- 
tained in  M ;  therefore,  P  is  contained  in  W. 

In  Extensive  Quantity,  it  will  be  recollected,  a  term  always 
denotes  a  class  or  a  part  of  a  class  ;  while  in  Intensive  Quan- 
tity it  denotes  an  attribute  or  a  complement  of  attributes. 
And  the  formula  of  the  Categorical  Deductive  Syllogism 
would  be  explicated  in  Extensive  Quantity  thus  : 

1.  Affirmative :  The  class  W  contains  under  it  the  class 
M ;  the  class  M  contains  under  it  the  class  or  individual  P  ; 
therefore,  the  class  "VV  contains  under  it  the  class  or  individ- 
ual P. 

2.  Negative :  The  class  W  does  not  contain  under  it,  en- 
tirely excludes,  the  class  M ;  the  class  M  contains  under  it 
the  class  or  individual  P  ;  therefore,  the  class  W  does  not 
contain  under  k  the  class  or  individual  P. 

In  Intensive  Quantity  it  would  be  explicated  thus : 

1.  Affirmative:  The  attribute  W  contains  in  it  as  part 
the  attribute  M ;  the  attribute  M  contains  in  it  as  part  the 
attribute  P  ;  therefore,  the  attribute  W  contains  in  it  as 
part  the  attribute  P. 

2.  Negative :  The  attribute  W  contains  in  it  the  attribute 
M  ;  the  attribute  M  does  not  contain  in  it,  entirely  excludes, 
the  "attribute  P;  therefore,  the  attribute  W  does  not  contain 
the  attribute  P. 

While  the  entire  reasoning  as  expressed  in  the  ordinary 
forms  of  discourse  may  be  explicated  in  either  quantity,  it 
would  plainly  be  incorrect  to  explicate  a  part  of  it  in  one 
quantity  and  the  rest  in  the  other  quantity; — to  explicate, 
for  instance,  one  premise  in  Extensive  Quantity,  and  the 
other  premise  or  the  conclusion  in  Intensive  Quantity. 


112  PURE  LOGIC 

§  70.  An  Inductive  Syllogism  is  a  Mediate  Reason- 
induction  mS'  m  which  the  movement  of  Thought  is  from  a 
defined.  given  part   to  its   complementary  part ;  as,  Affir- 

mation is  Thought ;  but  negation  is  the  complementary  of  affir- 
mation ;  therefore,  negation  is  Thought :  P  is  W ;  G  is  com- 
plementary of  P ;  therefore,  C  is  W. 

We  have  found  two  general  relationships  in  Thought  as  a 
relative  cognition,  each  equally  primitive  and  ne- 

Explication.  °     ...  .   n         J    r 

cessary,  coordinate,  and,  moreover,  conditioning 
each  the  other.  They  stand,  indeed,  in  this  respect,  precisely 
on  the  footing  of  the  two  Laws  of  Identity  and  Contradic- 
tion in  their  relations  to  the  two  Laws  of  Disjunction  and 
Exclusion.  The  one  relationship  is  that  of  Whole  to  Part ; 
the  other  is  that  of  Part  to  Part.  That  there  is  a  part,  in- 
volves the  necessity  of  there  being  another  part  or  parts, 
which  one  part  or  which  several  parts  are  the  complement 
of  the  first.  We  have,  then,  standing  side  by  side  with  the 
principle  that  the  whole  contains  its  parts,  the  coordinate 
principle  that  a  part  necessitates  in  Thought  its  complement- 
ary part. 

Now  this  complementary  part  is,  in  some  respects,  identi- 
cal with  the  other  part ;  in  other  respects  it  is  different  from 
it.  Just  so  far  as  they  are  parts  of  the  same  whole  they  are^ 
identical ;  but  so  far  as  they  are  complementary  of  each  other 
they  are  different.  If  two  triangles  are  parts  of  the  same 
square  bisected  through  its  opposite  angles,  they  are  identi- 
cal in  respect  of  length  of  sides,  angles,  surface  ;  they  are 
different  in  being  complementary  parts,  the  one  lying  in  one 
direction  from  the  bisecting  line,  the  other  in  the  opposite 
direction  from  that  line  ;  in  short,  they  are  as  complementary 
to  each  other,  related  as  positive  or  affirmative  and  nega- 
tive in  reference  to  the  principle  of  bisection.  What  is  thus 
evident  in  an  Integrate  Whole,  is  equally  true  in  the  Whole 
of  Substance.  If  rational  and  animal  are  the  component 
parts  of  man,  then  so  far  as  they  are  parts  of  the  same 
whole,  they  are  identical ;  that  is,  if  as  a  part  of  man,  as 


REASONINGS.  113 

living  substance,  rational  is  living,  we  necessarily  infer  that 
animal,  as  such  part,  is  also  living.  As  complementary  of 
each  other  they  are  different ;  animal  is  the  irrational  part 
of  man.  In  like  manner,  in  a  Causal  Whole,  if  ashes  and 
smoke  are  complementary  parts  of  the  effect  of  combustion 
conceived  as  a  whole,  then,  in  some  respects  —  for  instance,  as 
products  of  combustion  —  they  are  identical;  in  other  re- 
spects, as  complementary,  they  are  different ;  one  is  the  solid, 
the  other  is  the  non-solid  —  the  gaseous  product  of  com- 
bustion. In  a  logical  Whole  of  Extension,  the  two  species 
which  in  the  strict  dichotomous  division  make  up  its  parts, 
are  of  course  complementary  of  each  other.  They  are  iden- 
tical in  so  far  as  they  participate  in  the  whole  ;  they  are  dif- 
ferent in  so  far  as  they  are  conspecies.  Interpreting  animal 
thus  in  Extensive  Quantity,  that  is,  as  denoting  a  class,  we 
have,  as  two  species  contained  under  it,  rational  animals 
and  irrational  animals,  that  is,  men  and  brutes.  Now  what- 
ever is  true  of  men  so  far  as  animal,  is  true  of  brutes  so  far 
as  animal.  This  follows,  indeed,  necessarily,  from  the  very 
nature  of  a  Concept.  On  the  other  hand,  in  so  far  as  they  are 
conspecies,  and  accordingly  complementary  of  each  other, 
they  are  different.  In  so  far  as  man  is  rational,  man  is  differ- 
ent from  brute.  And  it  is  plain  that  whatever  part  of  what 
is  merely  animal  is  in  man  must  belong  to  whatever  like  part 
is  animal  in  brute  ;  while  whatever  part  of  rational  is  found 
in  man  differs  from  whatever  like  part  pertains  to  brute. 
And  here,  in  strictly  logical  or  dichotomous  division,  difference 
is  contradiction ;  so  that  we  may  infer  that  if  man  has  a 
digestive  system  necessarily  as  animal,  brute  has,  as  animal, 
a  like  system  ;  and  on  the  contrary,  if  as  rational  man  is 
free,  brute  as  irrational  is  not  free.  The  same  view  holds 
good  of  Intensive  Quantity  so  obviously  as  to  require  no 
distinct  consideration.  The  validity  of  this  kind  of  thought 
here  discovers  its  ready  and  certain  test.  If  our  Concepts 
in  which  we  reason  are  valid,  our  Induction  is  so  likewise. 
Such  is  the  simple  nature  of  all  Induction  as  a  process  of 
8 


114  PURE  LOGIC. 

Thought.  It  is  a  clearly  distinguishable  process  from  De- 
duction, and  is  precisely  coordinate  with  that  process  —  its 
exact  complement  as  a  derivation  of  a  Judgment.  It  gives 
the  character  of  absolute,  apodictic  certainty  to  its  result. 
Extremely  simple  as  it  is,  it  imparts  all  there  is  of  certainty 
or  of  probability  to  that  infinite  diversity  of  inferences  in 
scientific  investigations,  in  art-contrivances,  in  common  life, 
which  we  call  by  this  name  of  Induction  —  a  far  wider  move- 
ment of  thought,  as  already  observed,  and  far  more  impor- 
tant, every  way,  than  its  coordinate,  Deduction.  It  is  to 
that,  what  Addition  is  to  Subtraction  in  Arithmetic  ;  and  the 
two,  Induction  and  Deduction,  are  to  all  our  multifarious 
thinking  what  Addition  and  Subtraction  are  to  all  the  possi- 
ble and  complicated  operations  in  the  limitless  sphere  of  nu- 
merical calculation.  And  as  no  such  calculation  has  any 
validity  except  on  the  principle  that  one  added  to  one  equals 
two,  so  all  our  induction  in  its  multifarious  forms  is  valid  only 
on  the  principle  that  a  part  necessitates  its  complement.  We 
discover,  here,  moreover,  an  exact  analogy  to  the  logical  proc- 
ess of  Disjunction.  While  Logic  strictly  validates  only 
Contradictory  Opposition  in  Disjunction,  as  of  absolute  ne- 
cessary certainty,  yet  it  shows  how  Contrary  Disjunction  may 
be  validated  by  reduction  to  Contradictory,  and  thus  enables 
us  to  secure  the  character  of  truth  to  those  concise  and  com- 
plicated movements  in  which  Thought  in  common  life  gener- 
ally proceeds,  just  as  Multiplication  is  a  concise  complicated 
process  of  Addition.  So  in  Induction,  while  Logic  strictly 
accepts  only  the  immediate  relationship  in  thought  of  Part 
and  its  Complementary  Part,  it  yet  shows  how  far  this  move- 
ment may  be  validated  in  the  relationship  of  any  Part  to 
any  other  of  manifold  Parts  in  the  same  Whole. 

As  in  Deduction,  in  precise  logical  strictness,  we  can  rea- 
son only  step  by  step  down  the  gradations  of  parts,  in 
regular  succession,  and  must  always  be  able,  in  order  to  val- 
idate our  reasoning,  to  indicate  each  gradation,  but  yet  may 
reason  to  a  remote  part  of  a  part  —  may  leap  down  over 


REASONINGS.  115 

many  steps  in  a  single  movement  of  Thought :  so  in  Induc- 
tion, extremest  logical  rigor  requires  us  to  reason  only  to  one 
complementary  part ;  yet  it  allows  us,  while  maintaining  our 
ability  to  verify  our  procedure  by  a  reference  to  this  its 
single  ultimate  principle,  to  reason  to  remote  gradations  of 
complementary  parts.  Thus,  as  in  Deduction,  if  rational  be 
part  of  concept  man  ;  and  intelligent,  part  of  rational ;  and 
discriminative,  part  of  intelligent ;  and  comparative,  part  of 
discriminative,  we  may  safely  conclude  that  man  is  compara- 
tive, through  any  middle  —  rational,  intelligent,  discriminative 
—  although  to  verify  our  procedure  we  must  go  through  each 
successive  gradation ;  so  in  Induction,  if  rational  be  comple- 
ment of  animal ;  and  intelligent,  as  part  of  rational,  be  com- 
plement of  moral ;  and  discriminative,  as  part  of  intelligent, 
be  complement  of  intuitive  ;  then  we  may  infer  by  induction 
that  if  animal  is  living,  then  the  remote  ^complement  of  a 
remote  part  of  rational,  which  we  have  assumed  to  be  the 
complement  of  animal,  is  also  living.  The  principle  is  the 
same  as  in  the  process  when  limited  to  the  first  gradation, 
and  validates  as  of  absolute  certainty  the  abbreviated  pro- 
cess. Indeed,  we  have  here,  as  it  has  been  indicated  to  be 
with  Multiplication  in  respect  to  Addition,  only  a  compen- 
dious method  of  thought,  which  we  can  test  and  validate  only 
by  a  full  exposition  of  the  process  into  the  full  and  formal 
statements  of  the  Syllogism. 

All  Induction,  thus,  is  in  its  essential  nature  a  Mediate 
Reasoning,  in  which  the  agreement  or  difference  between  two 
objects  of  thought  is  recognized  through  their  respective  rela- 
tion to  a  third.  While  in  Deduction  the  thought  moves  from 
Whole  to  Part,  in  Induction  it  moves  from  Part  to  Part.  In 
strictest  logical  accuracy  these  two  parts  are  exactly  and 
fully  complementary  of  each  other,  making  up  one  whole  of 
thought.  But  as  we  may  have  valid  thought  proceeding  in 
contrary  opposition  as  well  as  in  contradictory  which  is  the 
strictly  logical  opposition,  so  we  may  have  valid  thought  in  the 
relations  of  any  part  of  one  of  these  two  primitive  complement- 


116  PURE  LOGIC. 

aries  to  any  like  part  of  the  other.  Indeed,  as  most  of  our 
thinking  is  in  fact  in  contrary  rather  than  in  contradictory 
opposition,  so  likewise  most  of  our  thinking  is  in  fact  in  the 
relationship  between  the  lower  gradations  of  parts.  And  as 
we  validate  thought  in  contrary  opposition  by  reducing  it  to 
contradictory,  so  likewise  we  validate  reasoning  in  the  rela- 
tions of  the  lower  gradations  of  parts  by  reducing  it  to  those 
between  the  two  primitive  complementaries. 

Under  the  Postulate  that  has  been  enounced,  §  18,  all 
valid  Induction  may  be  expressed  in  the  formal  Inductive 
Syllogism.  This,  like  the  Deductive,  contains  three  Prop- 
ositions which  have  as  their  subjects  and  predicates  three 
and  only  three  terms. 

Of  these  three  Terms,  two  are  parts  that  are  complement- 
ary of  each  other;  and  one  of  these  two  is  the  mediating 
term  of  the  reasoning,  and  may,  hence,  properly  be  called 
the  Middle  Term.  The  other  two  are  the  Extremes,  that 
which  denotes  the  whole  being  the  Major  Term,  and  that 
which  denotes  the  part  being  the  Minor  Term.  The  terms 
may  conveniently  be  indicated  by  the  letters  W,  P,  and  C ; 
of  which  W  denotes  the  major  term,  P  the  minor,  and  C  the 
middle  term. 

Of  the  three  Propositions,  two  are  given.  They  express 
the  data  to  the  thought  in  the  Reasoning.  They  constitute 
the  antecedent  of  the  syllogism,  and  are  called  the  Premises. 
The  other  expresses  the  derived  judgment  in  the  Reasoning} 
or  the  Consequent.     It  is  called  the  Conclusion. 

Of  the  two  Premises,  one  expresses  the  relation  between' 
the  middle  term  and  that  one  of  the  extremes  which  ex- 
presses the  whole.  It  may  be  called  the  Major  Premise,  or, 
better  perhaps,  the  Sumption.  The  other  premise  expresses 
the  relation  between  the  middle  term  and  the  other  extreme 
as  its  complementary.  It  may  be  called  the  Minor  Premise, 
or  the  Subsumption. 

The  Conclusion  expresses  the  relation  between  the  ex- 
tremes. It  is  signalized  by  the  illative  conjunction  therefore, 
and  its  synonyms. 


REASONINGS.  117 

The  formula  of  the  Inductive  Syllogism  will  thus  be : 
Sumption  :    G  is  W ; 

Subsumption  :  P  is  complementary  of  C ; 
Conclusion  :    Therefore,  P  is  W. 

Exemplifications  in  concrete  matter,  and  in  the  two  kinds 
of  Quality,  Affirmative  and  Negative,  may  be  given  thus : 

I.  Affirmative  Inductive  Syllogism. 

Sumption:  The  Inferior  Planets  (C)  shine  by  reflected 
light  (  W)  ; 

Subsumption :  The  Superior  Planets  (P)  are  complement- 
ary of  the  Inferior  Planets  (  0)  ; 

Conclusion  :  Therefore,  the  Superior  Planets  (P)  shine  by 
reflected  light  ( IF). 

This  syllogism  may  be  thus  explicated :  — 

Sumption:  The  middle  term  (C)  Inferior  Planets  is  part 
of  the  major  term  (W),  the  whole  class  of  things  shining  by 
reflected  light ; 

Subsumption :  The  minor  term  (P)  Superior  Planets  is 
complementary  of  the  middle  term  (C)  Inferior  Planets  ; 

Conclusion:  Therefore,  the  minor  term  (P)  Superior 
Planets  is  part  of  the  major  term  (W),  the  whole  class  of 
things  shining  by  reflected  light. 

II.  Negative  Inductive  Syllogism. 
Sumption  :    Venus  does  not  revolve  about  the  earth  ; 
Subsumption:    Uranus  is  a  planet  like  Venus; 
Conclusion  :   Therefore,  Uranus  does  not  revolve  about  the 

earth. 

The  exposition  which  has  thus  far  been  given  of  the  In- 
ductive Syllogism  has,  for  the  sake  of  clearness  and  simplic- 
ity, recognized  it  as  proceeding  only  in  Extensive  Quantity. 
But  it  is  equally  valid  in  Intensive  Quantity ;  and  the 
change  is  exactly  correspondent  to  that  already  indicated  in 
the  Deductive  Syllogism. 

We  have  accordingly  the  two  kinds  of  Inductive  Reason- 
ing distingished  in  respect  of  the  logical  quantity  of  the 
terms :  The  Extensive  Inductive  Syllogism,  and  the  Inten- 
sive Deductive  Syllogism. 


118  PURE  LOGIC. 

It  will  not  be  necessary  to  give  examples  of  the  Intensive 
form ;  for  those  already  given  may  be  easily  explicated  in 
this  kind  of  quantity. 

From  the  fact  that  European  logicians,  perhaps  by  reason 
of  the  omission  of  Aristotle,  the  lather  of  European  logic, 
to  elaborate  any  system  of  Inductive  as  he  did  of  Deductive 
Reasoning,  have  recognized  only  Deductive  in  their  exposi- 
tions and  illustrations,  the  formal  characters  of  the  Inductive 
Reasoning  are  not  so  familiar  to  our  minds  as  those  of  the 
Deductive.  Indeed,  but  for  the  disproportionate  elaboration 
of  Deduction  during  the  rise  and  early  progress  of  European 
literature,  shaping  and  coloring  all  its  forms  of  expression, 
the  full  form  of  the  Deductive  Syllogism  would  undoubtedly 
be  as  strange  to  us  as  that  of  the  Inductive  ;  for  our  ordinary 
thought  does  not  flow  in  full  logical  forms — one  of  the  prem- 
ises heing  generally  omitted  in  reasoning.  In  Inductive  rea- 
soning, the  Subsumption  is  hardly  ever  expressed.  It  is  the 
proper  function  of  Logical  Science  to  supply  what  is  thus 
implied,  thereby  to  validate  the  Thought. 

Induction,  moreover,  is  used  rather  in  the  investigation  of 
truth  than  in  probation,  which  is  more  closely  allied  to  De- 
duction. Its  nature  and  validity  will  accordingly  be  more 
particularly  illustrated  under  Methodology.  See  also  Ap- 
pendix. 

§  71.  The  second  class  of  Mediate  Reasonings  we  have  in 
Conditional  general  terms  distinguished  from  the  first  or  Cate- 
—  what.  gorical  class,  by  this  peculiarity,  viz  :  that  in  this 
second  class  the  derivation  of  the  new  Judgment  is  effected 
through  a  Judgment  as  such  —  through  the  copula;  while 
in  the  first  class,  the  derivation  is  through  Concepts  as  such, 
in  the  channel  of  their  reciprocal  relations  as  Wholes  and 
Parts.  The  Categorical  Deductive  Syllogism  thus  derives 
the  new  Judgment  through  the  relation  of  its  terms  as  re- 
spectively whole  and  part  in  respect  to  another  term  called  by 
virtue  of  this  twofold  relation,  middle,  and  the  Categorical 
Inductive  Syllogism  derives  the  new  Judgment  through  the 


REASONINGS.  119 

relations  of  its  terms  as  respectively  the  whole  and  the 
complementary  of  another  term  which  is  called  by  virtue  of 
this  relation  middle.  In  the  Categorical  Syllogism,  thus,  the 
reasoning  is  mediated  through  a  term —  a  Concept.  But,  as 
we  might  anticipate  as  altogether  a  probable  result,  the  medi- 
ation of  the  new  Judgment  may  be  effected  through  the 
proper  essence  of  the  Judgment ;  so  that  instead  of  a  Con- 
cept, a  Judgment  may  form  the  proper  middle  of  a  reasoning ; 
and  two  Judgments,  in  so  far  as  Judgments,  and  out  of  all 
regard  to  the  relations  of  their  terms,  may  stand  in  such 
relations  to  each  other,  that  Thought,  under  its  own  proper 
law  of  Identity  in  its  diverse  phases,  may  legitimately  move 
to  a  new  Judgment.  Such  is  the  case  in  that  class  of  Rea- 
sonings called  Conditional.  The  name,  it  may  be  observed, 
is  inadequate.  It  points  only  to  one  species  of  this  class  of 
Reasonings,  called  in  the  Greek,  Hypothetical,  a  word  ren- 
dered in  Latin,  Conditional.  If,  however,  it  be  borne  in  mind 
that  the  denomination  is  not  commensurate  with  what  is  de- 
noted by  the  name,  that  it  is,  as  in  many  other  cases  in  lan- 
guage, founded  on  only  a  part  of  the  object  meant,  no  serious 
evil  will  arise  from  continuing  the  use  of  the  appellation  ; 
probably  less  evil,  indeed,  than  would  arise  from  attempting 
an  innovation  on  a  received  nomenclature. 

A  Conditional  Syllogism,  then,  is  one  in  which  the  new 
Judgment  or  Consequent  is  derived  through  the  relation  of 
the  copulas  of  the  Antecedent  Judgments  ;  as,  If  A  is,  B  is  ; 
but  A  is,  therefore  B  is  ;  A  is  B  or  C;  but  A  is  B ;  there- 
fore A  is  not  C. 

§  72.  [nasmuch  as  every  Judgment  is  essentially  an  Affirm- 
ative or  a  Negative,  it  might  be  anticipated  that  Their  t 
there  would  be  two  modes  of  mediating  a  conclu-  modes- 
sion  through  the  copula  according  as  it  should  be  affirmative 
or  negative.  There  are,  in  fact,  accordingly,  two  modes  of 
reasoning  through  the  copula  —  the  one  is  called  the  Affirm- 
ative, the  Ponent,  or  the  Constructive,  as,  If  A  is,  B  is  ;  but  A 
is  ;  therefore  B  is  ;  the  other,  the  Negative,  the  Tollent,  or 


120  PURE  LOGIC. 

the  Destructive,  as,  If  A  is,  B  is  ;  but  B  is  not ;  therefore,  A 
is  not. 

§  73.  We  have  distinguished  two  kinds  of  Quality :  — 
Their  two  Simple  Quality,  the  two  complementary  kinds  of 
kinds:  Hy-     which  are  Affirmative  aud  Negative  ;  and  DHunc- 

pothetical  .  ......       ~      ,.         . 

aud  Disjunc-   tive   Quality.      On  this  distinction  in  Quality  is 

tivc. 

grounded  a  distinction  of  Conditional  Syllogisms 
into  the  two  kinds  of  Hypothetical  and  Disjunctive.  A  Hy- 
pothetical reasoning,  like  a  Categorical,  thus,  always  moves  in 
Simple  Quality  ;  while,  at  the  same  time,  it  differs  from  a  cate- 
gorical reasoning  in  that  it  is  mediated  through  a  Judgment, 
not  through  a  Concept.  A  Disjunctive  Reasoning,  on  the 
other  hand,  differs  from  both  in  that  it  moves  characteristically 
in  Disjunctive  Quality. 

§  74.  A  Hypothetical  Syllogism  is  a  Mediate  Reason- 
Hypotheticai  U1g  m  which  a  new  Judgment  is  mediated  from  a 
ftegene^i  Hypothetical  through  the  copula  of  a  Condition- 
nature.  ing  Judgment. 

The  Sumption  in  this  kind  of  Syllogism  is  a  Hypothetical 
Judgment,  or  one  in  which  the  subject  and  predicate  are 
Judgments,  and  which  accordingly  affirms  that  these  two 
Judgments  stand  in  the  relation  of  logical  Whole  and  Part, 
or  of  Part  to  Complementary  Part  to  each  other,  that  is,  as 
conditioning  and  conditioned.  The  Subsumption  may  affirm 
or  deny  the  Conditioning  Judgment ;  accordingly  the  Reason- 
ing may  be  in  either  one  of  two  modes,  the  Affirmative  or 
Negative.  And  the  Conclusion  will  be,  accordingly,  an  affirm- 
ation or  negation  of  one  of  the  members  of  the  Sumption, 
as  in  the  following  example  :  — 

Common  Sumption  —  If  A  is,  then  B  is. 

Ponent  Mode.  Tollent  Mode. 

Subsumption  :  But  A  is  ;  Subsumption  :  But  B  is  not  ; 

Conclusion  :  Therefore,  Bis.       Conclusion:   Therefore   A   is 

not. 


REASONINGS.  121 

Common  Sumption :  If  Socrates  is  virtuous,  he  merits  esteem. 

Ponent  Mode.  Tollest  Mode. 

But  Socrates  is  virtuous  ;  But  Socrates  does  not  merit 

Therefore,  he  merits  esteem.  esteem  ; 

Therefore,  he  is  not  virtuous. 

In  the  Ponent  or  Affirmative  Mode  the  conclusion  is  from 
the  truth  of  the  antecedent  to  the  truth  of  the  consequent ; 
while  in  the  Tollentor  Negative  Mode  the  conclusion  is  from 
the  denial  of  the  consequent  to  the  denial  of  the  antecedent. 

We  cannot  conversely  conclude  either  from  the  denial  of  Ccn^^-r^U^ 
the  antecedent  to  the  denial  of  the  consequent,  or  from  the 
affirmative  of  the  consequent  to  the  affirmative  of  the  ante- 
cedent, as  will  be  apparent  from  an  example.  From  the  Hy- 
pothetical Sumption:  If  the  sun  has  risen  it  is  light  in  the 
hall ;  we  cannot  conclude  from  a  denial  of  the  antecedent 
member  that  the  sun  has  risen,  that  it  is  not  light  in  the  hall ; 
for  the  hall  may  be  light  from  some  other  luminary.  Neither 
can  we  any  more  by  affirming  the  consequent  member,  it 
is  light  in  the  hall,  conclude  by  affirming  the  antecedent  mem- 
ber, the  sun  has  risen. 

It  appears,  then,  that  the  antecedent  clause  conditions  or 
determines  only  positively,  while  the  consequent  clause  con- 
ditions only  negatively.  The  reason  of  this  is,  that  the 
Sumption  must  affirm  a  determination  of  the  consequent  by 
the  antecedent,  or  there  would  be  only  a  negative  —  a  zero  — 
upon  which  to  suspend  the  reasoning.  But  it  is  of  the  very 
nature  of  this  determination  that  the  consequent  is  conditioned 
by  the  antecedent.  If  no  consequent  is  conditioned  there  can 
be  no  antecedent  conditioning.  To  deny  the  consequent  is, 
accordingly,  to  deny  the  antecedent.  But  the  Sumption  does 
not  condition  the  antecedent  upon  the  consequent  member  ; 
consequently,  we  are  not  authorized  from  affirming  the  con- 
sequent to  affirm  the  antecedent. 

A  regular  and  perfect  Hypothetical  Syllogism  must  con- 
tain three  propositions  :  a  Sumption,  Subsumption,  and  Con- 


122  PURE  LOGIC. 

elusion.  The  Sumption  must  be  an  affirmative  Hypothetical 
Proposition,  affirming  the  agreement  between  two  judg- 
ments. The  Subsumption  may  be  affirmative  or  negative  ; 
but  it  must  either  affirm  the  truth  of  the  antecedent  member 
of  the  Sumption,  or  deny  the  truth  of  the  consequent  member. 
If  the  Subsumption  be  affirmative,  the  conclusion  must  affirm 
the  truth  of  the  consequent  member  of  the  Sumption  —  the 
Ponent  mode ;  if  the  Subsumption  be  negative,. the  conclu- 
sion must  deny  the  antecedent  member  of  the  Sumption  — 
the  Tollent  mode. 

§  75.  As  a  Hypothetical  Judgment  may  be  either  simple 
or  disjunctive,  so  the   sumption  of  a   Hypothetical 

Two  kinds  of     0    .,      .  ,  .  ,  .        ,  ,.  . 

Hypothetical   syllogism  may  be    either   simple    or  disjunctive. 
y  ogism.       rp^  gjveg  rjge  to  a  division  inj0  {ne   two  clasSes 

distinguished  in  reference  to  this  quality  in  the  sumption  : 
1.  The  proper  Hypothetical,  of  which  we  have  just  given  an 
exposition,  and,  2.  The  Hypothetico-Disjunctive,  otherwise 
called  the  Dilemma,  as,  Whether  A  is  B  or  is  C,  D  is  E ;  but 
A  is  B  or  is  G ;  therefore,  D  is  E. 

The  Dilemma  was  a  great  favorite  with  the  Sophists,  as 
from  the  complexity  of  elements  that  enter  into  it,  a  fallacy 
may  easily  be  disguised  or  veiled  from  the  notice  of  an 
adversary.  It  has  also  received  very  prominent  attention 
from  logicians,  who,  however,  have  erred  in  ranking  it  as  a 
coordinate  class  with  Hypothetical  and  Disjunctive  Reason- 
ings. In  so  far  as  it  is  a  reasoning,  it  is  purely  Hypothetical, 
the  derived  judgment  being, mediated  independently  of  the 
disjunction  ;  it  is,  consequently,  to  be  ranked  as  a  subdivision 
of  Hypothetical  Reasonings. 

•  §  76.  If,  when  the  characteristics  of  the  Hypothetical  and 
The  Diiem-  °^ tne  Disjunctive  Judgment  are  combined,  the  dis- 
ma-  junction  appears  only  in  the  consequent  or  predi- 

cate member,  as  in  the  form,  If  an  action  be  prohibited,  it  is 
prohibited  either  by  natural  or  by  positive  law,  the  varia- 
tion from  the  proper  hypothetical  is  not  for  any  purposes  in 
thought  sufficiently  important  to  demand  any  special  treat- 


REASONINGS.  123 

ment.  But  if  the  disjunction  appear  in  the  antecedent  or 
subject  member,  we  have  a  class  of  judgments  of  peculiar 
interest  and  importance.  This  species  is  called  the  Dilem- 
matic  Judgment,  being  used  in  the  famous  reasoning  known 
as  the  Dilemma.  Its  form  is,  Whether  A  is  B  or  G  is  D,  E 
is  F ;  whether  it  melt  or  freeze,  the  road  will  he  rough.  We 
have  here  a  disjunction  of  judgments,  not  of  concepts  ;  and 
it  is  the  truth  of  one  or  the  other  of  the  alternative  judg- 
ments constituting  the  antecedent  on  which  the  truth  of  the 
whole  judgment  rests.  The  meaning  is,  either  alternative 
judgment,  that  it  will  melt  or  that  it  will  freeze,  involves  the 
judgment  that  the  road  will  he  rough. 

This  Judgment  is  properly  signalized  by  the  conjunction 
whether,  synonymous  with  if —  or. 

Its  forms  are  various.  In  the  first  place,  the  disjunction 
may  be  extended  to  more  than  two  members.  If  it  be 
carried  to  three,  the  reasoning  is  called  a  Trilemma  ;  if  to 
four,  a  Tetralemma ;  or  if  to  any  number  more  than  two, 
generally  a  Polylemma.  The  term  dilemma,  is,  however, 
applied  to  all,  whatever  the  number  of  disjunct  members  in 
the  sumption. 

In  the  next  place,  the  disjunction  may  be  either  in  the 
subject  or  in  the  predicate  of  the  sumption,  or  in  both  sub- 
ject and  predicate. 

In  the  third  place,  the  reasoning  may  be  either  in  the  Po- 
nent  or  the  Tollent  modes. 

In  any  of  the  forms,  the  Subsumption,  as  in  the  proper 
Hypothetical  Syllogism,  either  posits  the  antecedent  in  order 
in  the  conclusion  to  posit  the  consequent,  or  sublates  the  con- 
sequent in  order  to  sublate  the  antecedent.  The  reasoning 
accordingly  turns  on  a  judgment,  and  is  mediated  through 
that.     It  is  thus  a  mediate  conditional  reasoning. 

The  true  historical  Dilemma,  as  a  reasoning  which  offers 
to  an  adversary  an  alternative  of  propositions,  the  so-called 
"  horns  of  a  dilemma,"  one  of  which  he  must  take,  is  that 
in  which  the  subsumption  is  a  disjunctive  proposition.     The 


124  PURE  LOGIC. 

first  and  the  fourth  of  the  forms  given  below,  are  exam- 
ples. 

The  following  are  exemplifications  of  different  forms  of 
the  Dilemma. 

1.  Ponent  Dilemma  with  disjunct  antecedent:  —  "Whether 
the  blest  in  heaven  have  no  desires  or  have  desires  that  are 
fully  gratified,  they  will  be  perfectly  content ;  but  they  either 
will  have  no  desires  or  will  have  them  fully  gratified  ;  there- 
fore, they  will  be  perfectly  content."  The  reasoning  pre- 
sented in  this  full  syllogistic  form,  would,  in  ordinary  dis- 
course, be  expressed  in  some  such  compendious  way  as  the 
following :  "  The  blest  in  heaven,  will  either  have  no  de- 
sires, or  if  they  have  desires,  must  have  them  fully  grati- 
fied, so  that  in  either  case  they  will  be  perfectly  content." 
The  formula  of  this  form  is,  Whether  A  is  B  or  G,  D  is  E ; 
but  A  is  B  or  G ;  therefore,  D  is  E. 

2.  Tollent  Dilemma  with  disjunct  antecedent :  —  "  If  it  had 
rained,  or  if  there  had  been  a  heavy  dew,  the  walks  would 
be  wet ;  but  the  walks  are  not  wet ;  therefore,  there  was 
neither  rain  nor  dew."  If  A  is  B  or  G,  D  is  E ;  but  D  is 
not  E ;  therefore,  A  is  neither  B  nor  G. 

3.  Ponent  Dilemma  with  disjunct  consequent :  —  "  If  the 
parallelogram  be  not  equal  to  the  triangle,  it  must  be  either 
greater  or  less ;  but  it  is  not  equal ;  therefore,  it  is  either 
greater  or  less."  If  A  is  B,  G  is  D  or  E ;  but  A  is  B ; 
therefore,  G  is  D  or  E. 

4.  Tollent  Dilemma  with  disjunct  consequent :  —  "  If  man 
is  incapable  of  progress  towards  perfection,  he  must  be 
either  a  divinity  or  a  brute  ;  but  man  is  neither  divinity  nor 
brute ;  therefore,  he  is  not  incapable  (=  is  capable)  of  prog- 
ress towards  perfection."  If  A  is  B,  G  is  D  or  E ;  but  G 
is  neither  D  nor  E  ;  therefore,  A  is  not  B. 

5.  Tollent  Trilemma:  —  "If  mind  and  matter  are  not 
essentially  diverse,  then  either  they  must  be  absolutely  iden- 
tical, or  there  is  no  such  existence  as  mind,  or  no  such  ex- 
istence as  matter ;  but  neither  of  these  three  suppositions 


REASONINGS.  125 

is  tenable ;  therefore,  mind  and  matter  are  essentially  dis- 
tinct." If  A  is  B,  then  C  is  D,  or  E,  or  F;  but  G  is  neither 
D,  nor  E,  nor  F ;  therefore,  A  is  not  B. 

§  77.  A  Disjunctive  Syllogism  is  a  Mediate  Season- 
ing in  which  a  new  judgment  is  mediated  through   u.  .     x. 

.  "       °  o       Disjunctive 

a  new  judgment  removing  the  disjunction ;  as,  A  is   Syllogism. 
B  or  is  C ;  but  A  is  B;  therefore,  A  is  not  C. 

It  comes  immediately  under  the  second  pair  of  the  four 
fundamental  Laws  of  Thought  —  those  of  Disjunction  and 
of  Exclusion.  In  this  respect,  it  differs  from  Categorical  as 
well  as  from  Hypothetical  Syllogisms,  neither  of  which  classes 
directly  recognizes  this  pair  of  Laws. 

It  is  composed  of  three  propositions,  of  which  the  Sump- 
tion is  a  Disjunctive  Proposition  ;  the  Subsumption  removes 
the  disjunction  in  the  Sumption,  which  may  be  effected  in 
either  of  the  two  ways  of  affirming  or  denying,  giving  rise  to 
two  modes,  the  Ponent  or  Affirmative,  and  the  Tottent  or 
Negative ;  and  the  conclusion  denies  or  affirms  the  member 
not  subsumed. 

The  Sumption  of  a  Disjunctive  Syllogism,  as  ever  a  Dis- 
junctive Proposition,  admits  of  the  three  gradations  of  logi- 
cal opposition:  1.  Pure  logical  contradiction,  lying  in  the 
copula,  as,  A  is  B  or  is  not  B ;  2.  The  looser  logical  contra- 
diction, in  which  the  opposition  lies  in  the  terms,  as,  A  is  B 
or  non-B ;  animals  are  vertebrate  or  invertebrate;  and,  3.  Con- 
trary opposition,  as,  A  is  B  or  G. 

The  Sumption  is  necessarily  always  affirmative,  as  we  can 
conclude  nothing  from  a  mere  zero  of  thought ;  much  less 
from  an  impossibility  in  thought,  as  is  the  case  in  the  pure 
Contradictory  Disjunctive. 

Now,  as  a  Disjunctive  Proposition,  from  its  very  nature,  in 
its  strictest  form  respects  two  members,  either  of  which  may, 
supposably,  but  only  one  of  which  can,  actually,  be  recog- 
nized as  true,  it  is  clear  that  the  new  judgment — the  con- 
clusion —  may  be  mediated  through  the  removal  of  the  dis- 
junction either  by  affirming,  positing,  or  by  denying,  sublat- 
ing,  one  of  the  two  disjunct  members.     We  may,  from  the 


126  PURE  LOGIC.      " 

Disjunctive  Sumption  A  is  B  or  is  not  B,  either  conclude 
by  affirming  —  positing  one  member  to  a  denial  —  a  subla- 
tion  of  the  other,  or  conversely,  by  sublating  one  to  a  positing 
of  the  othei\  There  emerge,  thus,  two  distinct  kinds  of 
Disjunctive  Syllogisms. 

1.  The  Affirmative,  Ponent,  or  Positing,  (modus  ponens, 
modus  ponendo  tollens,)  in  which  one  of  the  disjunct  members 
is  posited  in  the  Subsumption  and  the  other  sublated  in  the 
Conclusion,  as,  A  is  B  or  C ;  hut  A  is  B ;  therefore,  A  is 
not  C. 

2.  The  Negative,  Tollent,  or  Sublating,  (modus  tollens, 
modus  tollendo  ponens,)  in  which  one  of  the  disjunct  members 
is  sublated  in  the  Subsumption  and  the  other  posited  in  the 
Conclusion;  as,  A  is  B  or  C;  but  A  is  not  B;  therefore, 
A  is  C. 

It  is  obvious  that  either  of  the  disjunct  members  may  be 
posited  or  sublated  in  the  Subsumption  ;  and  that  the  number 
of  disjunct  members  need  not  be  restricted  to  two.  But  in 
case  there  are  more  than  two,  they  must  be  taken  as  consti- 
tuting but  two  parts,  one  part  of  them  being  the  complemen- 
tary of  the  other.  Thus,  if  we  have  a  Sumption  in  the  form 
A  is  B,  or  C,  or  D,  or  E,  and,  in  the  Subsumption,  posit  B, 
we  sublate  C,  D,  and  E,  which  three  together  make  up  the 
complementary  of  B.  Or,  if  we  posit  B  and  C,  then  we 
sublate  D  and  E,  which  are  the  complementary  of  the  posited 
part  of  the  disjunct  members.  The  general  principle  in  all 
disjunctive  reasoning  is  that  by  positing  one  part  we  sublate 
the  complementary  part,  and  by  sublating  the  one  part  we  posit 
the  complementary  part. 

It  will  be  seen  from  this  exposition  of  the  nature  of  a  dis- 
junctive reasoning,  that  the  removal  of  the  disjunction  in  the 
sumption  is  essential.  Consequently  if  there  be  no  such 
removal  of  the  disjunction,  although  the  sumption  may  be 
a  Disjunctive  Proposition,  we  have  no  disjunctive  reasoning. 
Thus  the  following  is  not  a  Disjunctive  but  a  Categorical 
Syllogism :  A  is  B  or  C ;  but  D  is  A  ;  therefore,  D  is  B 
or  G. 


REASONINGS.  127 

The  Disjunctive  Syllogism,  moreover,  may  proceed  in  either 
quantity,  Extensive  or  Intensive.  Unless  the  special  forms 
appropriated  to  the  one  or  the  other  of  these  two  kinds  of 
logical  quantity  are  employed,  the  reasoning  may  generally 
be  explicated  in  either  with  equal  facility. 

The  following  examples,  one  in  abstract,  the  other  in  con- 
crete matter,  will  sufficiently  illustrate  the  peculiar  character 
of  a  disjunctive  reasoning  when  expounded  in  the  complete 
form  of  a  Disjunctive  Syllogism  :  — 

Common  Sumption  :  A  is  either  B  or  G  or  D. 
Ponent  Mode. 
Subsumption  :  But  A  is  B  ;  Or,  A  is  either  B  or  G. 
Conclusion  :    Therefore,  A  is  neither  G  nor  D  ;  Or,  There- 
fore, A  is  not  D. 

Tollent  Mode. 

Subsumption  :  But  A  is  not  B  ;  Or,  A  is  neither  B  nor  G. 
Conclusion:   Therefore,  A  is  either    G  or  D ;  Or,  There- 
fore, A  is  D. 

Common  Sumption :  The  ancients  were  in  genius  either 
superior  to  the  moderns,  or  inferior,  or  equal. 

Ponent  Mode. 
Subsumption:  But  the  ancients  were  superior  to  the  moderns. 
Conclusion  :   Therefore,  they  were  neither  inferior  nor  equal. 

Or,      . 
Subsumption  :   But  the  ancients  were  either  superior  or 
equal. 

Conclusion  :   Therefore,  they  were  not  inferior. 

Tollent  Mode. 
Subsumption  :  But  the  ancients  were  not  inferior. 
Conclusion  :   Therefore,  they  were  either  superior  or  equal. 

Ok, 
Subsumption :  But  the  ancients  were  neither  inferior  nor 
equal. 

Conclusion :   Therefore,  they  were  superior. 


128  PURE  LOGIC. 

It  is  plain  that  we  may  explicate  the  syllogism  in  either 
Quantity  with  equal  readiness;  thus,  in  Extensive  Quantity, 
the  class  ancients  is  contained  under  the  class  superior  to 
the  moderns,  or  under  the  class  inferior,  &c. ;  in  Intensive 
Quantity,  the  attribute  notion  ancients  contains  in  it  the  attri- 
bute sicperior  to  the  moderns,  or  the  attribute  inferior,  &c. 

§  78.  When  the  antecedent  of  a  mediate  reasoning  consists 
of  more  than  two  judgments  related  to  each  other  The  Polysyl. 
as  wholes  and  parts,  or  as  parts  and  complemen-  losism- 
tary  parts,  the  reasoning  is  called  a  Poly  syllogism,  also,  a 
Chain  of  Reasoning ;  in  respect  to  which  other  mediate 
reasonings  are  called  Monosyllogisms. 

A  Polysyllogism  is,  in  truth,  only  a  series  of  single  syllo- 
gisms, and  may  always  be  resolved  into  as  many  single 
reasonings  as  there  are  middle  terms  in  the  series.  Thus  the 
Polysyllogism  G  is  D;  Bis  G;  A  is  B  ;  therefore,  A  is  D, 
consists  of  two  single  syllogisms,  there  being  two  middle 
terms  B  and  C,  thus:  1°.  G  is  D;  B  is  C;  therefore,  B  is 
D.  2°.  B  is  D ;  A  is  B ;  therefore,  A  is  D.  Or,  in  con- 
crete matter,  the  Polysyllogism  :  An  animal  is  a  substance  ; 
a  quadruped  is  an  animal ;  a  horse  is  a  quadruped  ;  there- 
fore, a  horse  is  a  substance,  may  be  thus  resolved  into  two 
monosyllogisms ;  there  being  two  middle  terms,  animal  and 
quadruped.  1°.  An  animal  is  a  substance  ;  a  quadruped  is 
an  animal;  therefore,  a  quadruped  is  a  substance.  2°.  A 
quadruped  is  a  substance  ;  a  horse  is  a  quadruped ;  there- 
fore, a  horse  is  a  substance. 

It  appears  from  this  illustration  that  the  polysyllogism  is 
equally  valid  as  the  single  syllogism.  It  differs,  in  fact,  from 
a  series  of  single  syllogisms  in  which  the  conclusion  of  one 
becomes  a  premise  in  another  of  the  series,  only  in  the  par- 
ticular that  it  omits  the  useless  mention  of  this  connecting 
proposition.  If,  in  the  example,  we  simply  leave  out  of  the 
single  syllogisms  the  connecting  proposition  which  is  the  con- 
clusion of  the  first  and  the  sumption  of  the  second  —  a  quad- 
ruped is  a  substance  —  we  have  the  polysyllogism  as  in  the 
first  presented. 


REASONINGS.  129 

It  is  obvious,  also,  that  the  polysyllogism  may  equally  as 
the  monosyllogism  move  in  either  quantity,  Extensive  or  In- 
tensive. 

Moreover,  the  reasoning  may  be  progressive  or  regressive. 
That  is,  the  single  syllogisms  which  make  up  the  chain  may 
either  of  them  be  placed  first ;  the  order  of  statement  being 
as  truly  immaterial  as  in  the  case  of  the  premises  of  a  single 
syllogism.  If  the  conditioning  syllogism  be  placed  first,  we 
have  the  Progressive  chain  ;  if  the  dependent  syllogism  be 
placed  first,  we  have  the  Regressive  chain.  In  truth,  accord- 
ing as  we  explicate  the  reasoning  in  the  one  or  the  other 
quantity,  we  have  the  Progressive  or  the  Regressive  series. 
Thus,  if  we  explicate  the  example  in  Extensive  Quantity, 
we  have  the  Progressive  series  :  An  animal  is  part  of  the 
class  substance  ;  a  quadruped  is  part  of  the  class  animal ;  a 
horse  is  part  of  the  class  quadruped ;  therefore,  a  horse  is 
part  of  the  class  substance.  The  first  single  syllogism  here 
furnishes  the  sumption  for  the  second.  But  explicated  in 
Intensive  Quantity,  the  reasoning,  in  the  order  in  which  its 
parts  are  stated,  is  Regressive.  Thus  :  1.  Animal  contains 
the  attribute  substance ;  quadruped  contains  the  attribute 
animal;  therefore,  quadruped  contains  the  attribute  sub- 
stance. 2.  Quadruped  contains  the  attribute  substance; 
horse  contains  the  attribute  quadruped ;  therefore,  horse  con- 
tains the  attribute  substance.  Here  the  conclusion  of  the  first 
syllogism  furnishes  the  subsumption  of  the  second.  In  other 
words,  the  order  of  the  two  single  syllogisms  is  in  this  last 
explication  reversed,  inasmuch  as  the  subsumption  is  placed 
before  the  sumption,  while  in  the  more  natural  order  it  should 
be  placed  after  the  sumption.  Whether  the  series  is  Pro- 
gressive or  Regressive,  is  a  matter  of  no  moment,  so  far  as 
the  validity  of  the  reasoning  is  concerned. 

§  79.  The  Polysyllogism  has  been  distinguished  in  respect 
of  the  form  of  statement,  into  two  kinds :  the  Epichirema 
and  the  Sorites. 

The  Epichirema  is  a  polysyllogism  in  which  one  or  more 
9 


130  PURE  LOGIC. 

of  the  single  syllogisms  which  compose  it  is  immediately 
attached  to  one  of  the  premises,  thus :  Animal  is  a  substance; 
a  horse  is  an  animal,  for  it  is  a  quadruped ;  therefore, 
a  horse  is  a  substance  ;  or,  A  quadruped  is  a  substance,  for  it 
is  an  animal ;  but  a  horse  is  a  quadruped;  therefore,  a 
horse  is  a  substance. 

The  attached  syllogism,  which  as  in  reasoning  generally  is 
presented  elliptically  and  not  in  the  full  verbal  form  into 
which  every  thought  may  be  required  by  our  fundamental 
Postulate  to  be  explicated,  may  obviously  be  joined  to  either 
premise  or  to  both,  and  may  itself  be  a  polysyllogism  or  only 
single. 

The  Sorites  is  a  Polysyllogism  in  which  the  single  syl- 
logisms which  compose  it  are  presented  in  equally  indepen- 
dent relationship  to  the  whole  series.  It  is  sufficiently  exem- 
plified in  the  examples  given  of  the  Polysyllogism.  Indeed, 
it  is  the  regular  form,  while  the  Epichirema  is  the  irregular 
form  of  the  Polysyllogism,  into  which  the  former  may  always 
be  changed  without  affecting  the  nature  of  the  reasoning. 

§  80.  The  Polysyllogism,  further,  may  be  Categorical  or 
Conditional,  which  may,  moreover,  be  in  either  form  —  the 
Sorites  or  the  Epichirema. 

The  Categorical  species  has  been  sufficiently  treated  in  the 
general  exposition  already  given  of  the  Polysyllogism. 

The  Conditional  Polysyllogism  embraces  the  two  varieties 
of  the  Hypothetical  and  the  Disjunctive. 

It  will  be  sufficient  to  give  exemplifications  of  these  varie- 
ties without  more  extended  explanations.  It  is  only  necessary 
to  add,  that  they  may  proceed  in  either  Quantity  —  Exten- 
sive or  Intensive ;  that  they  may  be  Ponent  or  Tollent ;  that 
the  series  may  be  Progressive  or  Regressive  ;  that  the  num- 
ber of  links  in  the  chain  is  limited  only  by  the  considerations 
of  clearness  and  facility  of  expression  ;  and  that  they  respec- 
tively come  under  the  control  of  the  principles  which  regu- 
late the  higher  classes  of  reasoning  to  which  they  severally 
belong,  and  may  always  be  resolved  into  single  syllogisms. 


REASONINGS.  131 

Hypothetical  Sorites  :  If  Harpagon  be  avaricious,  he  is 
discontented;  if  he  is  discontented  he  is  unhappy;  now 
Harpagon  is  avaricious  ;  therefore,  he  is  unhappy. 

Hypothetical  Epichirema  :  If  Harpagon  is  avaricious, 
he  is  intent  on  gain  ;  if  he  is  intent  on  gain  he  is  unhappy, 
for  he  is  discontented ;  now  Harpagon  is  avaricious ; 
therefore,  he  is  unhappy. 

Disjunctive  Sorites:  A  Science  is  either  Pure  or  Induc- 
tive ;  a  Pure  Science  is  either  Mathematical  or  Logical; 
but  Astrology  is  neither  Mathematical,  nor  Logical,  nor  In- 
ductive ;  therefore,  Astrology  is  not  a  Science. 

Disjunctive  Epichirema  :  All  Science  is  either  Pure  or 
Inductive  ;  a  Pure  Science  is  either  Mathematical  or  Logi- 
cal, for  it  treats  either  of  the  Conditions  of  Thought  or 
the  Elements  of  Thought ;  but  Astrology  is  neither  Math- 
ematical, nor  Logical,  nor  Inductive  ;  therefore,  Astrology 
is  not  a  Science. 


PURE    LOGIC. 

PART   II. 

METHODOLOGY. 


CHAPTER  I. 

METHOD   IN    GENERAL. 

§  81.  "  Method  in  general  is  the  regulated  procedure  to- 
Method—  wards  a  certain  end;  that  is,  a  process  governed 
■what.  by  rules,   which   guide    us    by   the    shortest   way 

straight  towards  a  certain  point,  and  guard  us  against  devious 
aberrations.  Now  the  end  of  Thought  is  Truth,  Knowledge, 
Science  —  expressions  which  may  here  be  considered  as  con- 
vertible. Science,  therefore,  may  be  regarded  as  the  perfec- 
tion of  thought,  and  to  the  accomplishment  of  this  perfection 
the  Methodology  of  Logic  must  be  accommodated  and  be 
conducive." 

But  while  Science,  thus,  is  the  proper  end  of  all  Thought, 
and  Logical  Method  must  have  reference  to  Thought  as  its 
one  end,  it  is  still  to  be  regarded  only  as  the  immediate  end, 
which  may,  itself,  be  modified  and  controlled  by  still  higher 
ends.  In  fact,  Science  or  Truth  may  have  its  end  either  in 
itself — in  the  True,  or  in  the  Beautiful,  or  in  the  Right  and 
Good ;  and  the  Method  of  Thought  will  vary  in  some  re- 
spects with  this  specific  remoter  end.  Still  further,  the 
Method  of  Thought  will  vary  with  the  more  specific  ends 
under  each  of  these  higher  governing  ends.  We  may  deal 
with  Thought  for  the  purpose  of  acquiring  knowledge,  or  for 


METHOD   IN   GENERAL.  133 

the  purpose  of  communicating  knowledge  ;  and  the  Method 
requisite  for  the  Investigation  of  Truth  will  so  far  vary  from 
the  Method  requisite  for  the  Communication  of  Truth. 

In  like  manner  the  Method  of  Thought,  as  governed  by 
the  higher  end  of  guiding  to  the  Beautiful,  will  vary  specif- 
ically, as  the  particular  end  is  the  Contemplation  or  the  Cre- 
ation of  the  Beautiful. 

So,  too,  we  have  a  specific  variation  in  the  Method  of 
Thought,  where  the  governing  idea  is  the  Right  or  the  Good, 
according  as  Subjective  or  Objective  Rectitude  or  Goodness 
is  the  particular  end. 

It  is  sufficient  to  point  out  here  these  modifications  of 
Logical  Method  in  respect  to  these  several  general  ends  in 
thinking.  The  full,  detailed  consideration  of  them  belongs 
either  to  Modified  Logic  or  to  Applied  or  Special  Logic. 
Pure  Logic  confines  itself  to  the  domain  of  Truth  in  itself — 
Science  for  its  own  sake. 

§  82.  Science,  farther,  as  true  or  certain  knowledge,  sup- 
poses  two   conditions.     Of  these,  the  first  has  a   Threefold 
relation  to  the  object  known;  the  second,  to  the   offence: 
knowing  subject.    Moreover,  it  cannot  be  accepted   Material, 

„  "  lormal,  and 

as  fully  perfected  until  properly  embodied  in  Lan-   Verbal, 
guage.     We  have  thus  determined  to  us  the  threefold  Per- 
fection of  Science  —  Material,  Formal,  and  Verbal. 

Now  as  Logic  is  a  Science  exclusively  conversant  about 
the  form  of  thought,  it  would  seem  that  it  could  take  into 
account  only  the  former  of  these  two  elements  —  the  formal 
perfection  of  thought.  And  in  a  certain  sense  this  is  a  cor- 
rect inference.  Only,  in  fact,  so  far  as  the  form  is  necessarily 
dependent  on  the  object  of  thought,  only  so  far  as  its  formal 
perfection  must  of  necessity  regard  the  matter,  does  Pure 
Logic  look  to  the  matter  of  Thought.  Were  Logic  to  shut 
out  from  its  view  all  consideration  of  the  matter  of  Thought, 
it  would  be  reduced  to  such  meagre  proportions  as  to  be  un- 
worthy of  the  name  of  a  science,  and  barren  of  all  utility ; 
much  as  would  be  the  case  with  Geometrical  Science  if,  be- 


134  PURE  LOGIC. 

cause  a  pure  formal  Science,  it  were  to  exclude  from  its  con- 
sideration all  distinctions  of  its  object,  such  as  Lines,  Surfaces, 
and  Solids,  Rectilineal  and  Curvilinear  Surfaces,  and  the 
like.  The  truth,  the  objective  reality  of  its  matter,  indeed,  a 
purely  formal  Science  does  not  regard.  The  conclusions  of 
Mathematical  Science  are  equally  sound  whether  there  be 
space  or  not ;  whether  space  be  a  proper  entity  or  a  mere 
form  of  our  thinking  ;  whether  there  be,  indeed,  extension, 
that  is,  extended  matter  in  space  or  not.  It  only  supposes 
this  or  that  in  regard  to  its  matter,  —  space,  extension,  —  as- 
sumes it  or  accepts  it  as  given  to  it.  So  Logic  only  assumes 
its  matter  or  accepts  it  as  given  to  it  by  other  sciences.  Yet 
inasmuch  as,  if  we  think,  we  must  think  of  something,  and 
that  something  must  be  viewed  as  standing  in  a  necessary 
relation  to  our  thought,  so  thought  must  be  necessarily  differ- 
ent, if  carried  beyond  the  most  shadowy  abstractions,  as  its 
object  differs.  Logic  will  then  so  far  regard  the  matter  of 
thought  as  to  see  that  it  is  possible  to  think  it  and  to  think  it 
correctly.  As  Thought  regards  Being  as  its  object,  and  as 
Being  is  necessarily  apprehended  in  the  two  aspects  of  Sub- 
stance and  Cause,  and,  if  apprehended  at  all,  must  be  appre- 
hended in  one  of  these  two  aspects,  the  proper  Logical 
Perfection  of  Thought  requires  that  this  twofold  considera- 
tion be  taken  of  Being.  Logic  does  not  assume  it  into  her 
province  to  prove  the  reality  of  Being  as  either  Substance 
or  Cause.  She  only  assumes  or  accepts  it  as  given  to  her, 
and  deals  with  it  as  if  real.  Her  laws  are,  consequently, 
just  as  valid  to  the  pure  Idealist  as  to  the  Realist.  But  she 
necessarily  demands  that  what  is  given  her  be  so  given  as 
that  her  capacities  of  receiving  may  lay  hold  of  it ;  and  so 
far  she  must  assure  herself  in  regard  to  Being  that  it  is 
shaped  to  her  capacities,  conformed  to  her  nature.  Being, 
even  ideal  Being,  can  be  nothing  to  Logic,  except  as  appre- 
hended in  this  seen  correlation  to  her  proper  functions,  which 
are  simply  and  characteristically  functions  of  Quantity,  mov- 
ing only  in  the  relations  of  Whole  and  Parts.     Farther  than 


METHOD  IN  GENERAL.  135 

this,  Logic  needs  to  apprehend  Being  in  order  to  verify,  to 
illustrate,  to  apply  her  laws.  Her  growth,  if  growth  she 
could  be  supposed  to  have,  would  be  only  the  shadow  of  an 
abstraction  unless  allowed  in  Being.  There  could  be  no  illus- 
tration, no  exemplification.  Moreover,  the  utility  of  Logic, 
and  well-nigh  its  whole  worth  to  man,  lies  in  the  possibility 
of  its  being  applied  to  the  objects  with  which  he  is  conver- 
sant. If  not  so  developed  as  to  be  readily  and  habitually  ap- 
plied to  the  realities  of  human  life,  logical  science  could  only 
be  regarded  as  a  toy,  a  bubble,  brilliant  and  beautiful  it  may 
be,  but  worthless,  instead  of  being,  as  it  should  be,  the  chief- 
est  guide  and  helper  to  all  intellectual  growth  and  culture. 

Logic,  then,  must  so  far  deal  with  the  matter  of  Thought 
as  to  be  able  to  verify  its  applications  to  Being,  both  as  Sub- 
stance and  as  Cause.  It  must  view  them,  indeed,  only  in  the 
relations  of  proper  Identity  and  Quantity  —  of  Whole  and 
Parts.  But  it  must  view  the  parts  of  Substance  in  a  some- 
what different  light  from  the  parts  of  Cause.  It  must  regard 
the  parts  of  the  former  as  Attributes  in  the  narrower  sense, 
and  those  of  the  latter  as  Effects  —  Effects  in  its  fullest 
sense.  As  Thought  proceeds  differently,  although  under  the 
self-same  laws,  when  applied  to  the  two  respectively,  Logic 
must  be  able  to  follow  these  different  pi'ocedures  with  assur- 
ance of  being  right  in  its  regulation  of  them. 

Logical  Science  has,  for  the  most  part,  regarded  only  Sub- 
stance, and  although  it  has  used  the  term  attribute  to  denote 
whatever  can  be  predicated  of  a  subject,  it  has  in  its  illustra- 
tions identified  the  term  with  the  parts  of  a  Substance,  and 
has  seemed  to  ignore  utterly  the  parts  of  a  Cause.  Indeed, 
the  reputed  father  of  the  Science,  Aristotle,  himself  seems  to 
think  Substance  and  Cause  convertible  in  all  predication  ; 
and  in  this  he  has  been  followed  by  subsequent  logicians. 
Thus  the  proposition,  "  The  Romans  conquered,"  is  alleged 
to  be  convertible  with  the  proposition,  "  The  Romans  were 
victorious."  But  this  is  to  confound  "  action  "  with  "  quality," 
the  one  being  predicable  only  of  "  Cause,"  the  other  only  of 


136  PURE  LOGIC. 

"  Substance."  And  the  obscurities  and  errors  which  have 
followed  from  the  confusion  have  been  not  less,  nor  of  less 
importance,  than  those  which  have  followed  from  the  con- 
founding of  the  two  species  of  Logical  Quantity  —  Compre- 
hensive and  Extensive.  They  are  no  less  serious  than  what 
might  he  supposed  to  follow  from  confounding  lines  with  sur- 
faces in  geometry,  as  has  been  done  by  some  who  through 
this  fallacy  have  fancied  they  have  solved  the  great  problem 
of  the  Quadrature  of  the  Circle. 

It  will  not  be  amiss  to  recapitulate  the  principles  which, 
as  we  have  seen,  cover  the  relations  of  Thought  to  its 
matter. 

1.  The  object-matter  of  Thought  is  a  duality  of  cognitions. 

2.  These  cognitions  are  viewed  in  Thought  only  in  the 
relation  of  Same  and  Different,  or  derivatively,  as  Wholes  or 
Parts. 

3.  Such  cognitions  as  Wholes  or  Parts  are  of  different 
kinds  which,  in  order  to  perfect  knowledge,  Thought  must 
distinguish.  There  are  two  generic  divisions  of  Wholes  — 
(1.)  Those  of  Thought  itself.  (2.)  Those  external  to  Thought. 

4.  The  Wholes  of  Thought  are  either —  (1.)  Conditions  of 
Thought,  as  the  Affirmative  and  the  Negative,  which,  as  Com- 
plementary Parts,  make  up  what  may  be  called  The  Dianoetic 
Whole  ;  or,  (2.)  Products  of  Thought,  the  Wholes  of  Compre- 
hension and  Extension,  called  Logical  Wholes. 

5.  The  Wholes  external  to  Thought  are  —  (1.)  Those  of 
Forms  of  Being,  called  Integrate,  comprising  the  two  species 
of  Spacial  and  Numerical.  (2.)  Those  of  Being  itself,  sub- 
divided, in  reference  to  the  two  modes  of  Being,  into  (or.) 
Substantial,  and  (b.)  Causal. 

§  83.  The  Material  Perfection  of  Science  involves  in  its 
Two  virtues  largest  import  the  reality  of  the  matter,  as  well  as 
l^er/wtiouof  tne  correctness  of  the  thought.  We  distinguish  in 
Science  —      a\\  Science,  in  all  Thought,  three  elements :    the 

Adequateness  '  . 

andAccu-       object  known,  the  knowing  subject,  and  the  act  of 
knowledge    itself.     Now  although  a*  science   can 


METHOD   IN   GENERAL.  137 

be  regarded  as  perfect  only  when  these  three  elements  are  in 
their  respective  perfection,  only  when  there  is  a  true  matter, 
a  true  intelligence,  and  a  true  knowledge,  Logic  —  Discur- 
sive Logic,  as  the  Science  of  the  Laws  of  Knowledge  as 
Knowledge  —  dismisses  the  two  related  extremes,  the  perfec- 
tion of  the  Matter  and  the  perfection  of  the  Intelligence, 
and  limits  itself  to  the  consideration  of  the  third  element  — 
that  of  the  relation  between  them.  It  leaves  to  the  proper 
Nomology  of  the  Presentative  Faculties  —  the  Nomology  of 
Perception,  the  Nomology  of  the  Regulative  or  Intuitive 
Faculty  —  to  prescribe  the  conditions  of  a  perfect  cognition  of 
the  matter  which  it  appertains  to  them  to  apprehend.  Such 
a  cognition  might  be  denominated  the  Material  Perfection 
of  Knowledge,  as  importing  only  that  the  matter  as  presented 
by  these  faculties  to  the  Discursive  Faculty  is  correctly  ap- 
prehended by  them  ;  that  is,  in  correspondence  with  its  true 
being.  But  the  Material  Perfection  of  Science  which  falls 
within  the  domain  of  Logic  is  widely  different  from  this. 
As  Thought  is  the  relation  between  the  Thinking  Subject 
and  the  Object  Thought,  which,  it  should  be  remembered,  is 
not  the  original  object  of  the  Presentative  Faculties,  but 
ever  a  cognition,  it  has  a  double  aspect,  looking  both  inward 
to  the  subject  and  outwrard  to  the  object.  Now,  Thought,  to 
be  perfect  in  this  outward  relation — in  relation  to  the  cog- 
nition presented  to  it  —  must  be  conformed  to  its  object.  It 
must  both  be  conformed  to  the  outer  limitations  of  the  mat- 
ter, be  conterminous  with  it,  be  adequate,  filling  out  the 
entire  field  of  the  matter  without  transcending  it ;  and  it 
must  also,  in  like  manner,  be  conformed  to  all  parts  or  con- 
tents of  the  object  —  must  be  accurate.  These  two,  then, 
are  the  two  virtues  comprised  in  the  Material  Perfection  of 
Science,  so  far  as  it  falls  within  the  domain  of  Logic  :  —  Ade- 
quateness  and  Accuracy. 

§  84.  The  Formal  Perfection  of  Science  comprises  three 
virtues  :  —  one  common  to  it  with  other  cognitions,  as  those 
of  Perception   and   Intuition,  founded   in   the   very  nature 


138  PURE  LOGIC. 

of  the  Intelligence,  viz  :  Clearness  ;  the  second,  founded  on 
Three  vir-  tne  general  characteristic  of  Thought  itself,  its 
mafperfw-"  relativeness,  viz:  Congruence,  otherwise  called 
fcioiiofSci-  Harmony  or  Agreement;  the  third,  on  the  spe- 
cieamess,       cific  characteristic  of  this  relativeness  in  Thought, 

Congruence,  . 

and  Distinct-  as  being  that  of  Whole  and  Parts,  viz  :  Distinct- 
ness. 

ness. 

The  one  Essential  Perfection  of  all  Intelligence,  viewed 
irrespectively  of  its  relations  to  its  objects,  is  Clearness.  A 
perfect  cognition  and  a  clear  cognition  are  convertible  ex- 
pressions, if  we  regard  cognition  only  on  its  purely  formal 
side  —  cognition  simply  as  cognition.  This  perfection  of 
Thought  is  determined  to  it,  then,  by  the  very  nature  of  the 
Intelligence  of  which  it  is  one  product. 

But  Thought  is  a  relative  cognition,  being  by  this  attribute 
of  relativeness  distinguished  from  other  products  of  the  In- 
telligence. That  there  should  be  this  relation  apprehended 
in  all  Thought  is  thus  indispensable  to  its  perfection.  The 
terms,  which  constitute  the  factors  in  this  relation,  must  be  in 
correlative  or  logical  harmony  —  must  be  congruent.  This 
is,  indeed,  but  the  principle  of  Identity  in  its  special  applica- 
tion to  Method. 

Once  more,  Thought  takes  cognizance  of  its  objects  only 
in  the  relations  of  Identity  or  Quantity.  It  deals  with 
Wholes  and  Parts.  Now  a  clear  cognition  of  the  parts  of  a 
whole  as  parts,  is  denominated  a  distinct  cognition. 

Clearness  thus  respects  the  outward  relations  of  an  object 
of  thought  —  its  relations  to  other  objects.  Distinctness  re- 
spects its  internal  relations  —  its  relations  to  the  parts  of 
which  it  is  composed. 

§  85.  All  human  science,  moreover,  stands  in  a  relation  of 
dependence,  more  or  less  entire,  upon  Language. 
fectionof        If  Language  must  be  admitted  to  be  the  product 
of  Thought,  it  is  yet  equally  undeniable  that  Lan- 
guage is  the  necessary  instrument  of  its  progress.     Thought 
not  only  works  through  Language  ;  it  also  exhibits  the  results 


METHOD  IN  GENERAL.  139 

of  its  operations,  step  by  step  in  its  endless  working,  in  lan- 
guage. And,  still  further,  it  contemplates,  criticises,  verifies 
its  work,  as  thus  exhibited  in  language.  Its  relationship  to 
language  appears,  thus,  to  be  most  intimate  and  vital.  It 
becomes  important,  therefore,  to  determine,  somewhat  more 
precisely  than  we  have  yet  done,  this  inter-dependence  be- 
tween Thought  and  Language,  in  order  to  ascertain  the  con- 
ditions of  perfect  science. 

The  object  of  Thought  as  an  activity,  we  have  found  to  be 
ever  a  cognition.     Thought  begins  with  a  cognition  as  the  ne- 
cessary prerequisite  of  its  movement.     Leaving  out  of  view, 
now,  those   cognitions  which  are  the  products  of  Thought 
itself,  and  which  are  presented  to  it  by  itself  as  the  objects 
of  its  activity,  the  primitive  original  objects  of  Thought  are 
the  simple,  individual,  or  irrelative  objects  of  the  Presentative 
and  Intuitive  Faculties.     With  these  objects  given  as  cogni- 
tions by  one  or  the  other  of  these  Faculties,  Thought  origi- 
nally  begins.      But   simultaneously    with    these    cognitions 
arising   in   the    consciousness,   the    process   of    naming,  of 
speech-making,  begins.     It  begins,  too,  there  can  be  no  reason 
to  question,  under  the  superintendence  of  the  principle  of  all 
Thought,  the  principle  of  Identity  ;  at  least,  we  must  believe, 
in  harmony  with  it.     Let  us   suppose,  now,  a  cognition  pre- 
sented through  the  Perceptive  Faculty,  through  the  sense  of 
sight,   for    example,  the   sun.      A   name  would,  under   the 
native  tendencies  of  the  human  soul,  at  once  be  given  it ; 
and  the  name  as  sound,  would  be  one  bearing  some  analogy, 
identical  in  some  respect,  with  some  other  accidental  modifi- 
cation of  the  consciousness  at  the  time.     We  may  imagine  it 
to  be  possibly  an  ejaculation  prompted  by  the  joy  which  the 
first  perception  of  the  sun  would  naturally  produce.     That 
ejaculatory   sound  would   naturally  furnish  the  materials  in 
sound  for  a  name  of  the  sun,  because  identified  with  its  first 
experience   of  that  object.     It  is  now  the  name  of  an  indi- 
vidual,   simple,    in   other  words,  irrelative  cognition.      But 
we  will  suppose  the  moon  subsequently  to  come  into  the  ex- 


140  PURE  LOGIC. 

perience,  producing  the  identical  effect  of  joy  in  kind  through 
its  common  attribute  of  brightness.  It  would  be  named  like 
the  first  —  be  designated  by  the  same  sound  in  speech.  But 
now  the  name  no  longer  denotes  a  single  object ;  it  denotes 
a  plurality  of  objects  identified  in  having  a  common  attribute 

—  brightness.  It  is  now  the  name  of  a  concept,  formed 
upon  the  predicate  Base  —  brightness.  We  will  suppose, 
further,  a  third  object  producing  the  same  effect,  a  star,  to 
enter  the  experience.  The  name  is  as  naturally  extended  to 
that.  The  star  is,  in  other  words,  gathered  into  the  class  on 
the  same  Base  ;  and  the  concept  is  enlarged  in  its  extension. 
Thus  the  process  goes  on  indefinitely  in  this  direction. 

But  we  will  now  suppose  another  attribute  to  be  given  in 
the  experience.  The  sun  is  perceived  to  be  round.  Bright 
and  round  are  now  apprehended  as  belonging  to  the  same 
subject  —  sun.  The  predicates  are  combined,  and  a  concept 
in  comprehension  is  the  result.  The  name  before  given  to 
the  concept  in  extension  is  now  found  to  denote  more  than 
one  attribute  ;  and  the  name  is  used  now  in  both  senses, 
denoting  Comprehension  as  well  as  Extension.  Other  attri- 
butes may  be  added,  and  thus  the  concept  may  grow  in  botli 
quantities  —  the  limit  being  always,  that  in  the  synthesis  of 
subjects  there  be  predicates  common  to  all ;  and  in  the  syn- 
thesis of  predicates,  there  be  subjects  to  which  they  all  in 
common  belong.  The  original  name  first  applied  to  denote 
the  irrelative  object,  sun,  thus  comes  to  denote  a  concept 
embracing  an  indefinite  number  of  objects  having  the  same 
complement  of  predicates,  and  also  embracing  an  indefinite 
number  of  predicates  all  concurring  in  each  of  the  subjects 

—  in  other  words,  a  Concept  with  exactly  correlative  quanti- 
ties of  Comprehension  and  Extension. 

But  in  the  progress  of  Experience  and  Thought,  another 
parallel  process  begins.  A  body  enters  the  experience 
which  is  bright,  and  which,  therefore,  at  first  might  have  been 
united  with  the  sun  into  a  concept  under  that  attribute  as 
common   to   both  objects,  but  it  is  not  round.     It   cannot, 


METHOD  IN  GENERAL.  141 

therefore,  be  gathered  into  the  class  of  bright  round  bodies. 
A  concept  is  now  formed  of  bodies  that  are  merely  bright, 
with  no  reference  to  figure  ;  and  a  name  to  signalize  the 
union  is  given  to  it —  say,  luminaries.  The  first  object,  sun, 
now  belongs  to  two  classes,  is  embraced  in  two  concents.  To 
indicate  it,  a  name  is  made  up  by  combining  so  many  of  the 
predicates  as  will  suffice  to  distinguish  it  from  other  objects 
embraced  under  the  concept.  Thus  arise  modifying  words 
or  adjectives ;  and  by  the  use  of  them  we  are  enabled  to  in- 
dicate in  language  the  primitive  individual  object  with  which 
the  process  began,  by  calling  it  the  sun,  or  the  great  heavenly 
luminary.  We  thus  clearly  separate  it  from  all  other  objects 
embraced  in  sun,  regarded  as  a  subject-concept  —  that  is,  in 
its  Extension  —  in  other  words,  define  it  by  the  use  of  certain 
adjectives,  called,  hence,  Definitives.  In  a  precisely  analo- 
gous way,  we  indicate  the  primitive  individual  attribute  or 
predicate.  We  say  the  bright  sun,  meaning  that  one  property 
of  the  complement  of  characters  that  have  been  gathered  into 
the  word  regarded  as  a  predicate  concept,  that  is,  in  its 
comprehension,  employing  here  certain  adjectives  called  in 
this  case  Epithets.  Or  convenience  or  occasions  of  use  may 
bring  in,  during  the  progress  of  speech,  a  new  word  derived 
from  some  other  language,  as  Phoebus,  or  suggested  by  some 
other  accident  in  experience.  And  from  this  word  may  start 
a  new  process  in  word-formation. 

Precisely  in  the  same  way  the  concept-word  may  be  nar- 
rowed to  a  species  only ;  that  is,  to  a  part  of  the  comprehen- 
sion, instead  of  being  carried  through  to  the  individual  attri- 
bute. Here,  too,  new  series  of  word-formations  may  origi- 
nate. 

Such  is  the  genesis  of  language,  so  far  as  concept-words, 
whether  concretes,  that  is,  subject-concepts,  or  abstracts,  that 
is,  predicate-concepts,  and  the  thought-element  in  them  are 
concerned.  The  consideration  of  the  genesis  of  the  sound- 
element  in  words  is  foreign  to  Logical  Science.1     ]t  appears 

»  i  See  Appendix  B. 


142  PURE  LOGIC. 

from  this  that  it  is  a  gross  error  to  suppose  that  Language  origi- 
nates with  general  ideas.  Such  ideas  are  the  product  of 
thought  alone,  and,  therefore,  presuppose  the  individual  cog- 
nition. Nothing  can  be  conceived  more  preposterous  than 
that  the  process  of  generalization,  from  which  alone  general 
ideas  can  arise,  precedes  the  cognition  of  individual  objects 
and  attributes.  Generalization  presupposes,  also,  the  naming 
of  these  individual  objects  and  attributes.  Moreover,  the 
instinctive  generalization  that  has  gone  on  in  the  genesis  of 
language,  has  been  step  by  step,  by  the  addition  of  one  object 
and  one  attribute  at  a  time.  It  may  be,  indeed,  that  that 
object  or  attribute  may  have  been  a  group  or  an  aggregate 
that  subsequently  has  been  found  to  embrace  a  plurality  of 
separable  objects  or  attributes,  but  when  first  apprehended  in 
thought  it  must  have  been  viewed  as  one  —  as  individual. 
To  trace  back  the  history  of  a  concept  word,  whether  con- 
crete or  abstract,  in  the  expectation  of  finding  a  generic  or 
comprehensive  cognition  at  the  origin,  is  to  proceed  in  contra- 
diction of  the  first  principles  of  thought.  Bright,  for  example, 
is  now  a  generic  appellation  ;  but  it  could  have  become  so 
only  by  being  found,  in  the  progress  of  Experience,  to  belong 
to  a  plurality  of  objects.  It  was,  if  we  may  assume  it  here 
to  be  a  primitive  word,  originally  given  as  a  property  of  an 
individual.  It  is,  also,  now,  a  composite  abstract,  embracing 
such  involved  characters  as  radiant,  undulating,  sense-im- 
pressing  ;  but  it  must  have  been  originally  simple,  and  could 
only  in  the  progress  of  experience  come  to  be  regarded  as  a 
composite. 

Now  it  is  apparent  from  this  summary  view,  that  only  the 
few  words  which  are  first  applied  to  designate  individual 
objects  and  simple  characters  or  attributes,  come  from  any 
other  faculty  than  that  of  thought ;  that  Thought,  as  the 
principle  of  Identity  in  all  acts  of  the  Intelligence,  presides 
over  the  first  naming  of  these  ;  that  these  names  of  individ- 
ual objects  and  simple  attributes,  begin  at  once  to  pass  into 
concepts,  which  are  the  pure  products  of  Thought,  and  even 


METHOD  IN   GENERAL.  143 

individual  objects  and  simple  attributes  come  to  be  designated 
by  concept  words  used  to  modify  one  another.    Thus  Language 
comes  finally  to  be  made  up,  to  a  large  extent,  of  words  which 
have  been  determined  as  to  their  meaning  and  use  by  Thought. 
But  the  view  we  have  taken  shows,  also,  that  Language  is 
not  less  the  instrument  than  the  product  of  Thought.      The 
results  of  previous  processes  of  Thought  are  taken  as  mate- 
rials and  conditions  of  new  processes.     Thought  takes  con- 
cepts already  formed,  and    combines   them  with  other  con- 
cepts, thus  forming  new  concepts,  and  still  new  combinations 
onward  indefinitely.     Now  it  is  obvious  that  as  the  concept 
must  always  maintain  the  exact  correspondence  between  the 
two  quantities  of  Comprehension  and  of  Extension,  and  as 
Thought  does  not  bring  up  in  review  all  the  individual  objects 
and  simple  characters  which  have  in  successive  combinations 
entered   into   the   concept,  there    must  be  great   liability  to 
error.     Moreover,  there  is  a  constant  tendency  for  the  very 
sake  of  precision  in  Thought,  to  narrow  the  import  of  words. 
Thus,  for  example,  the  word  Thought,  itself,  formerly  included 
in  its  meaning  all  acts  of  the  mind,  emotions  and  volitions, 
as  well  as  acts  of  Intelligence,  but  now  is  limited  to  the  acts 
of  one  of  the  Faculties  of  the   Intelligence.     Still  further, 
when  we  jay  Thought  has  shaped  Language,  we  use  meta- 
phorical diction.     Men,  thinkers,  individual  thinkers,  acting 
indeed  together  in   their  intercourse   with   each  other,  and 
under  common  regulative  principles,  have  produced  all  words, 
created  all   language.       Hence  the  extreme  necessity  that 
Thought,  as  it  presses  its  products  into  verbal  forms,  should 
be  aware  of  the  many  liabilities  to  error,  and  protect  itself 
against  them  as  far  as  may  be,  in  order  to  arrive  at  its  goal 
of  truth  or  perfect  science.     Only  when  it  has  verified  its 
incorporation  of  its  products  into  language  expressing  cer- 
tain truth,  can  it  be  assured  of  having  reached  this  its  goal. 
In  this,  is  attained  the  Verbal  Perfection  of  Science,  when 
Knowledge,  conformed   to  the  realities  of  things   as  appre- 
hended by  the  Presentative   Faculties,  and  shaped  into  its 


144  PUKE  LOGIC. 

own  essential  form  by  Thought,  appears  at  last  in  its  proper 
embodiment  of  language. 

To  recapitulate  these  views  of  the  relations  of  Thought  to 
Language : — 

1.  The  cognitions,  attained  by  the  Perceptive 
Language  to   and  Intuitive  Faculties,  of  individual  objects  and 

Thought;  as  .  .,  ,  "* 

Product,  as     ot  simple  attributes,  are  named  under  the  guidance 
and  as  Em-'    and  prompting  of  the  proper  principle  of  Thought 

bodiment.         _  tfaat  Qf  Identjty# 

2.  The  concepts,  elaborated  by  Thought  out  of  these 
primitive  cognitions,  which  make  up  the  great  body  of  notion- 
words  in  a  language,  are  expressed  in  language  in  words  de- 
rived from  the  names  of  those  primitive  cognitions,  and  are 
equally  under  the  guidance  of  Thought. 

3.  On  the  other  hand,  all  the  movements  of  Thought  are 
through  words ;  and  all  its  products  attain  to  permanent  life 
only  as  embodied  in  words.  Language  is  the  Instrument  as 
well  as  the  Embodiment  of  Thought. 

§  86.  The  Verbal  Perfection  of  Science,  implying  its  per- 
VerbaiPer-  feet  embodiment  in  Language,  involves  two  char- 
sdeDce°its    acters  or  virtues  :  —  1.  Correctness;  2.  Perspicu- 

nessand  Correctness  is  founded  upon  the  relations  of 

Perspicuous-  r 

ness.  Thought  to  its  outward   body,  language.     It  re- 

quires that  the  thought  be  truly  rendered  in  the  words  that 
express  it.     More  specifically,  correctness  requires  — 

1.  That  the  naming  of  the  primitive  cognitions  given  by 
the  Presentative  Faculties  to  Thought,  be  founded  on  some 
identity  cognizable  in  proper  Thought. 

2.  That  the  naming  of  concepts  be  founded  on  the  rec- 
ognized identity  in  respect  to  their  Base,  of  the  subjects  or 
of  the  predicates  which  are  respectively  combined  to  form 
the  concept. 

3.  Thnt  the  relations  of  the  Terms  in  Judgments  be  ex- 
pressed in  such  wise  as  truly  to  represent  the  specific  charac- 
ter of  the  Judgment,  and,  also,  the  specific  nature  of  the 
kind  of  whole  in  which  the  Judgment  moves. 


METHOD   IN   GENERAL.  145 

Perspicuodsness  is  founded  upon  the  essential  quality 
of  Thought  as  Intelligence,  viz.,  Clearness,  and  requires 
that  the  Thought  appear  clearly  through  the  verbal  expres- 
sion. 

Subordinate  qualities  of  Perspicuousness  are  Significance  ; 
Perspicuousness  Proper,  requiring  u.-e  of  unambiguous  words 
and  right  arrangement  of  relative  words  ;  and  Brevity. 

§  87.  It  is  evident  that  inasmuch  as  there  are  various 
products  of  Thought,  whose  perfection  must  re-  Divisions  of 
spectively  be  determined  by  their  bearing  these 
several  virtues  of  Thought  in  their  modified  applications, 
Logic  must  accommodate  its  Method  to  the  consideration  of 
these  virtues  in  detail,  as  they  pertain  to  these  several  prod- 
ucts of  Thought. 

The  products  of  Thought,  although  alike  the  products  of 
the  same  Faculty,  —  the  Discursive  Faculty  or  Faculty  of 
Comparison,  whose  essential  and  characteristic  function  it  is  to 
identify  what  is  common  to  a  plurality  of  objects,  —  vary,  as 
we  have  seen,  as  different  gradations  from  one  another.  The 
simplest  and  most  fundamental  of  these  gradations  is  the 
Judgment.  Now,  inasmuch  as  a  Judgment  is  the  identifica- 
tion of  an  attribute  or  character  as  belonging  to  an  object, 
the  Logical  Perfection  of  a  Judgment  is  attained  by  securing 
the  conditions  of  an  identification  of  the  attribute  or  charac- 
ter with  its  object.  The  determination  of  these  conditions 
will  accordingly  form  the  matter  of  a  Methodology  of  the 
Judgment. 

A  Concept,  being  produced  by  an  act  of  synthesis,  —  by 
combining  into  a  unity  the  several  subjects  identified  with  a 
common  predicate,  or  the  several  characters  or  attributes 
identified  with  a  common  subject,  —  will  attain  perfection  by 
securing  the  conditions  of  such  synthesis  or  combination. 
And  Methodology,  as  applied  to  this  element  of  thought,  will 
determine  and  indicate  these  conditions. 

A  Reasoning,  being  derived  from  a  Judgment,  either  by 
an  act  of  Transformation  or  of  Analysis,  will  attain  its  log- 
10 


146  PURE  LOGIC. 

ical  perfection  by  securing  the  conditions  of  this  transforma- 
tion and  analysis.  The  Methodology  of  Reasoning  will  ac- 
cordingly investigate  and  point  out  the  conditions  of  these 
two  modes  of  derivation. 

Logical  Methodology  will  thus  consist  of  three  depart- 
ments corresponding  with  the  three  Elements  of  Thought  : 
1.  The  Methodology  of  Judgments.  2.  The  Methodology  of 
Concepts.    3.  The  Methodology  of  Reasonings. 


CHAPTER  II. 

METHOD   IN    SPECIAL.  —  METHODOLOGY    OP  JUDGMENTS. 

§  88.  The  full  Perfection  of  a  Judgment  involves  the 
several  conditions  of  Material,  Formal,  and  Ver-  The  Three 

.  .  Conditions 

bal  Perfection,  as  these  virtues    may  character-   of  Perfection 
ize  an  identification  of  an  attribute  with  its  sub-  ments.° 
ject. 

These  three  conditions,  accordingly, —  1.  That  in  respect 
of  its  matter,  the  predicate  be  recognized  as  agreeing  with 
the  subject ;  2.  That  in  the  thought  this  identity  be  deter- 
mined or  declared  in  the  judgment ;  and,  3.  That  the  verbal 
statement  correspond  with  the  identity  as  thought,  —  are  the 
self-evident,  as  they  are  the  most  fundamental,  conditions  of 
a  perfect  proposition. 

In  regard  to  the  first  condition  lying  in  the  matter,  it  may 
be  remarked  that  it  is  not  fhcumbent  on  Logic  to  verify  the 
matter  that  is  originally  given  it  as  the  object  of  thought. 
But  when  matter  is  thus  given  and  the  Discursive  Faculty 
applies  its  energy  to  it,  what  is  given  must  be  treated  in  con- 
formity with  its  own  nature.  Thought  must  not  deal  with 
Being  as  if  it  were  only  Mathematical  Form.  Accepting 
the  formula  1=  1  as  mere  formula  expressive  of  the  identity 
of  every  object  of  Thought  with  itself,  it  must  not  then  con- 
vert this  form  without  content  into  form  with  content ;  in 
other  words,  surreptitiously  foist  in  Being  into  this  empty 
form,  and  flatter  itself  it  has  proved  the  reality  of  Existence. 
In  like  manner,  if  its  given  matter  be  Substance,  it  must 
not  in  the  handling  of  it  treat  it  as  if  Cause.  Thought 
must  comprehend  its  own  matter,  and  must  be  held  respon- 


148  PURE  LOGIC. 

sible  for  the  maintenance  of  its  purity  throughout  all  its 
processes. 

Hence  the  rule  that  the  Judgment  be  so  framed  that  in 
the  matter  as  given  by  the  Presentative  or  the  Representa- 
tive Faculties,  that  which  is  taken  as  subject  or  as  predicate 
be  clearly  recognized  in  accordance  with  the  kinds  of  whole 
in  which  the  matter  is  viewed.  No  rule  in  Method  is  more 
fundamental  than  this,  or  more  wide-sweeping.  It  would  be 
impossible  to  exclude  error  from  a  Judgment,  incongruence 
from  a  Concept,  or  fallacy  from  a  Reasoning,  except  on  this 
condition  :  that  the  Judgment  admit  of  a  ready  reference  of 
its  terms  to  its  matter  as  given,  so  far  as  the  kind  of  Quantity 
is  concerned,  for  a  verification  of  its  truth.  While  in  strict- 
ness Logic  takes  only  what  is  given,  and  is  concerned  purely 
with  the  form,  not  with  the  matter,  it  must  never  ignore  the 
relationship  of  form  to  matter,  and  must  order  its  procedures 
in  harmony  with  this  relationship.  The  principle  of  this  re- 
lationship is  that  of  Quantity.  That  we  can  think  any  object 
implies  that  the  object  contains  the  principle  of  Whole  and 
Parts  and  thus  answers  to  Thought,  which  moves  only  accord- 
ing to  this  principle.  The  two  virtues  of  Thought  to  be  se- 
cured by  this  Law  are  those  of  Adequateness  and  Accuracy. 
It  is  the  Objective  Law  of  adjudgment,  and  aims  at  the 
Material  Perfection  of  Science. 

The  next  rule  is  that  the  identity  between  the  Terms 
affirmed  in  the  Judgment  be  clearly  recognized.  This  is  the 
Subjective  Law  of  a  Judgment,  and  aims  at  the  Formal  Per- 
fection of  Science. 

The  third  rule  is  that  the  Language  in  which  the  Judg- 
ment is  embodied  be  recognized  as  truly  representing  the 
thought.  This  is  the  Verbal  Law  of  a  Judgment,  and  aims 
at  the  Verbal  Perfection  of  Science. 

The  distinct  enumeration  of  these  fundamental  Rules  of  a 
Judgment  is  important  both  to  correct  thinking,  and  also  to 
correction  of  error  in  the  results  of  thinking.  Only  as  the 
mind   has    become    habituated    to    discriminate  these   three 


METHODOLOGY  OF  JUDGMENTS.        149 

several  kinds  or  degrees  of  truth  in  a  proposition  —  corre- 
spondence of  the  notions  to  the  terms,  agreement  between  the 
terms,  and  correspondence  of  the  words  to  the  notions  —  can 
it  proceed  safely  in  the  exposition  of  its  thoughts.  And  only 
as  it  is  enabled  readily  to  distinguish  the  several  ways  in 
which  error  can  creep  into  its  thoughts,  can  it  verify  them  or 
purge  them  from  the  error  that  vitiates  them. 

§  89.  The  foregoing  are  the  general  conditions  or  rules  of 
a  perfect  Judgment.  We  proceed  to  those  that  Rules  ofNeg- 
are  special.  These  will  vary  according  to  the  DuJunTtiYe 
special  nature  of  the  several  kinds  of  Judgments.  Judsments- 
The  most  general  distinction  of  Judgments  is  in  respect  of 
their  essential  Quality,  as  Affirmative,  Negative,  or  Dis- 
junctive. The  Rules  for  the  Affirmative  Judgment  are  obvi- 
ously the  same  as  those  that  have  been  given  for  Judgments 
as  such.  The  Rule  for  the  Negative  Judgment  is,  that  the 
terms  of  the  Proposition  be  recognized  as  opposed  or  differ- 
ent —  as  non-identical.  Nothing  need  be  said  in  explication 
of  this  rule,  as  it  is  only  the  negative  phase  of  the  rule  for 
affirmative  Judgments. 

The  Disjunctive  Judgment  presents  peculiar  difficulties, 
and  requires  more  extended  consideration.  This  Judgment, 
it  must  be  borne  in  mind,  is  founded  on  the  third  and  fourth 
Laws  of  Thought,  the  Law  of  Disjunction  and  of  Exclusion 
or  Excluded  Middle,  which  obliges  us  to  think  that  of  two 
contradictory  attributes  one  must,  and  only  one  can,  belong  to 
the  subject.  The  obvious  condition  of  a  perfect  Disjunctive 
Judgment,  then,  is  that  the  disjunction  affirmed  be  a  true 
contradictory  disjunction. 

The  liability  to  error  in  forming  Judgments  of  this  class 
arises  from  the  inadequacy  of  Language  to  furnish  terms  for 
all  the  contradictory  oppositions  that  may  arise  in  Thought, 
and  the  resulting  necessity  of  a  recourse  to  the  so-called  op- 
position of  Contrariety,  which  gives  only  a  mediate  disjunc- 
tion. In  this  case,  to  secure  that  the  Judgment  be  a  perfect 
Judgment,  the  disjunction  will  need  to  be  carried  up  into  one 


150  PURE  LOGIC. 

of  contradictory  opposition.  For  illustration,  in  the  Disjunct- 
ive Judgment,  Angles  are  right,  acute,  or  obtuse,  we  test  the 
perfection  of  the  Judgment  by  applying  the  principle  of 
Contradiction  successively  to  the  several  pairs  of  disjunct 
members.  We  say,  first,  Angles  are  right  or  are  not  right  ; 
then  we  say,  Angles  that  are  not  right  are  acute  or  obtuse,  that 
is,  less  or  greater  than  right ;  and  in  this  way  attain  a  proper 
logical  or  contradictory  disjunction.  Only  so  far  as  we  can 
carry  through  this  contradictory  disjunction  between  the  mem- 
bers, can  we  have  the  logical  basis  of  a  perfect  Disjunctive 
Judgment. 

The  two  Rules,  then,  which  are  involved  in  the  conditions 
of  a  perfect  Disjunctive  Judgment,  are,  — 

First,  if  the  disjunction  be  one  of  two  members,  they  must 
be  recognized  as  contradictories  to  each  other. 

Secondly,  if  it  be  one  of  more  than  two  members,  the 
members  must,  by  being  properly  paired  with  each  other,  or 
with  others  to  be  supplied,  be  reducible  to  the  form  of  a 
series  of  Disjunctive  Judgments  of  Contradictory  Opposi- 
tion. 

As  disjunction  in  thought  and  disjunction  in  the  verbal 
expression  are  expressed  in  language  by  the  same  particles, 
or,  nor  ;  either,  or;  neither,  nor  ;  it  becomes  necessary  to  ap- 
prehend which  is  intended.  The  following  proposition  is 
equivocal :  Consequently  space  is  divided  from  itself  by  space, 
or  is  not  divided  at  all.  The  disjunction  may  be  interpreted 
to  apply  to  the  Judgment,  when  the  meaning  will  be,  Space 
either  is  divided  from  itself  by  space,  or  is  not  divided  at 
all ;  or  to  the  mode  of  expression,  when  the  meaning  will  be, 
Space  is  divided  from  itself  by  space,  in  other  words,  is  not 
divided  at  all. 

It  should  be  remembered  that  a  perfectly  pure  disjunction 
can  only  be  in  the  copula.  A  either  is  B  or  is  not  B,  is  not 
always  convertible  into  A  is  cither  B  or  non-B,  in  which 
the  disjunction  is  in  the  terms,  the  datum  of  the  Judg- 
ment. 


METHODOLOGY  OF  JUDGMENTS.        151 

§  90.  The  second  distinction  of  Judgments  we  found  to  be 
grounded  on  their  Modality.  The  conditions  of  a  Ruieg  rf 
perfect  Judgment  imposed  by  this  distinction  are  Modal  judg- 
that  its  character  as  Pure,  that  is,  assertory,  or 
as  Modal,  and  if  Modal,  as  Problematic  or  Apodictic,  be 
clearly  recognized.  The  special  liability  to  error  here  orig- 
inates in  the  fact  that  through  the  imperfections  in  language 
the  modality  of  the  judgment  which  lies  in  the  copula  alone, 
may  be  covertly  slipped  over  to  the  predicate.  Thus  the 
judgment,  Alexander  may  have  conquered  Darius,  is  easily 
converted  into  the  proposition,  Alexander  ivas  a  possible 
conqueror  of  Darius,1  which  is  a  very  different  proposi- 
tion ;  and  although  in  certain  uses  the  two  are  equivalent, 
in  other  uses  they  would  have  a  very  different  import.  The 
one  is  a  purely  concessive  proposition,  which,  from  its  nature, 
may  require  no  proof;  the  other  is  an  assertory  proposition, 
and  proof  may  reasonably  be  required  of  him  who  puts  it 
forward. 

The  several  species  of  Judgments  given  by  this  distinction 
differ  from  one  another  in  strength.  The  Apodictic  is  the 
strongest,  and  involves  the  Problematic  and  the  Assertory ; 
and  the  Assertory  involves  the  Problematic.  The  danger, 
therefore,  is  that  what  has  been  problematically  enounced 
should  be  mistaken  for  an  assertory  or  a  necessary  judgment ; 
or  that  a  mere  assertory  judgment  or  enunciation  should  be 
mistaken  for  an  apodictic  or  necessary  judgment. 

Further,  as  no  sensible  symbol,  no  sight  or  sound,  can  ade- 
quately express  a  purely  mental  act,  and  language  from  its 
felt  impotency  even  forbears  often  any  expression  of  the  act 
of  judging,  it  is  to  be  expected  that  the  distinctions  of  judg- 

1  It  is  remarkable,  to  illustrate  this  liability,  that  Sir  William  Hamil- 
ton calls  the  proposition,  Alexander  conquered  Darius  honorably,  a  Modal 
Proposition;  and  as  he  readily  converts  it  into  the  form,  Alexander  was 
the  honorable  conqueror  of  Darius,  when  the  modification  is  unquestion- 
ably one  of  the  predicate,  not  of  the  copula,  he  concludes  that  the  distinc- 
tion of  propositions  on  this  ground  of  modality  is  futile.  —  See  Lectures  on 
Logic,  xiv,  page  181.   Boston  edition. 


152  PURE  LOGIC. 

ments  in  themselves  would  be  left  subject  to  imperfect  and 
equivocal  means  of  expression.  The  forms  of  language  used 
to  denote  these  distinctions  are,  in  fact,  borrowed  from  those 
appropriated  to  other  uses.  It  becomes  necessary,  therefore, 
in  order  to  secure  correct  thought,  to  weigh  carefully  the 
language  in  which  it  is  conveyed  ;  —  to  apprehend  whether  the 
forms  used  do,  indeed,  express  modality  at  all,  and  if  so, 
whether  that  modality  is  adequately  determined  in  them.  The 
distinctions  of  modality  are  denoted  in  the  English  Language 
by  the  auxiliaries  may  or  can  with  their  respective  tense 
inflections  for  the  Problematic,  and  must  for  the  Apodictic 
Judgment ;  and  also  by  Adverbials,  as  possibly,  probably,  neces- 
sarily, and  the  like.  Now  all  these  modal  forms  may  attach  to 
the  matter  thought,  or  to  the  Thought  itself,  and  hence  arises 
the  equivocality  in  expressing  modal  distinctions.  Thus  in 
the  Judgment,  John  may  recover  in  a  month,  the  meaning 
may  be  that  his  disease  is  such  as  to  admit  of  his  recovery, 
and  the  Judgment  itself  be  strictly  assertory.  Or,  on  the 
other  hand,  the  contingency  may  lie  in  the  Judgment  itself. 
Although  in  ordinary,  loose  discourse,  it  may  answer  equally 
well  to  connect  the  contingency  with  the  predicate  or  with 
the  copula,  yet  correct  thinking  may  often  require  that  the 
distinction  be  clearly  noted. 

§  91.  The  third  distinction  of  Judgments  is  founded  on  the 
degree  which  is  regarded  in  the  determined  agree- 

Rules  of  b  °  ° 

Partial  ment  between  Subject  and  Predicate. 

The  conditions  of  a  Perfect  Judgment  imposed 
by  this  distinction,  are  :  — 

1.  That  the  Identity  affirmed  be  distinctly  recognized  as 
Total  or  as  Partial,  both  in  respect  of  Thought  and  of  Verbal 
Expression. 

2.  That  if  the  Identity  be  Partial,  the  precise  part  of  the 
containing  whole,  whether  it  be  in  the  Subject  or  in  the 
Predicate  which  the  affirmation  respects,  be  distinctly  recog- 
nized. 

§  92.  The  fourth  distinction  of  Propositions  is  into  the  two 


METHODOLOGY  OF  JUDGMENTS.        153 

species  of  Categorical  and  Hypothetical,  according   RulegofH 
as  the  whole   regarded   in  them  is  an    object   or  pothetioai 

°  Judgments. 

truth. 

The  first  condition,  then,  prescribed  by  this  distinction,  is 
that  the  Judgment  be  recognized  as  belonging  to  the  one  or 
to  the  other  of  these  species. 

The  difficulty  here  will  be  found  chiefly  with  the  Hypo- 
thetical Judgment,  in  discriminating  accurately  wherein  the 
identity  affirmed  in  the  Judgment  between  the  terms  lies,  as 
the  real  nature  of  the  Judgment  is  obscured  by  the  form  in 
which  it  is  expressed,  as  well  as  by  the  name  which  has  in- 
aptly been  given  to  it.  It  should  be  fully  understood  that 
there  is  nothing  more  conditional  or  hypothetical  in  the  nature 
of  a  Hypothetical  Judgment  than  in  any  other.  The  simple 
import  of  every  such  Judgment  is  that  the  truth  expressed 
in  the  subject,  or,  as  it  is  called,  the  first  or  antecedent  mem- 
ber, involves  or  conditions  the  truth  of  the  predicate  or  con- 
sequent member.  Now,  inasmuch  as  for  the  most  part  Prop- 
ositions in  discourse  are  only  expressions  of  a  partial  identity 
between  the  subject  and  the  predicate  —  only  affirm  that 
some  one  part  of  the  subject  is  identical  with  the  predicate, 
or  some  one  part  of  the  predicate  is  identical  with  the  sub- 
ject, or,  it  may  be,  some  one  part  of  the  subject  is  identical 
with  some  one  part  of  the  predicate,  —  the  liability  to  error  in 
the  so-called  Hypothetical  Judgment  is  far  greater  than  in 
the  case  of  a  Categorical  Proposition,  inasmuch  as  it  is  more 
difficult  to  identify  the  parts  of  a  truth  than  the  parts  of  an 
object.  The  hypothetical  form  of  the  Proposition,  moreover, 
disguises  the  true  nature  of  the  Judgment,  and  so  increases 
the  liability  to  error. 

This  dissection  of  the  Hypothetical  Proposition,  accord- 
ingly, prescribes  the  following  conditions  of  a  Perfect  Hypo- 
thetical Judgment :  — 

1.  It  must  be  clearly  apprehended  in  its  true  nature  as  a 
Judgment,  the  terms  of  which  are  Truths  or  Judgments,  not 
simple  objects  —  not  Concepts  nor  Integrate  Wholes. 


154  PURE  LOGIC. 

2.  The  specific  parts  in  the  terms  —  in  the  Antecedent  and 
the  Consequent  Members  —  between  which  the  identity  af- 
firmed lies,  must  be  distinctly  recognized,  as  also  the  truth  of 
these  members  as  themselves  judgments. 

3.  It  is  further  necessary  to  recognize  whether  the  Judg- 
ment is  in  the  relation  of  Whole  and  Part,  or  in  that  of  Part 
and  Complementary  Part. 

To  illustrate  the  application  of  these  conditions,  we  will  take 
the  Hypothetical,  proceeding  in  the  relation  of  Whole  and 
Part :  If  there  be  a  God,  the  world  is  governed  by  Provi- 
dence. The  first  condition  requires  that  we  distinctly  recog- 
nize the  proposition  as  one  in  which  the  terms,  here  called 
the  Antecedent  and  Consequent  Members,  are  Truths  or 
Represented  Judgments,  assumed  pro  hac  vice  to  be  true ;  as 
meaning,  in  other  words,  that  the  truth  that  a  God  is,  con- 
tains in  it  the  truth  that  the  world  is  governed  by  Providence. 
The  second  condition  requires  that  we  recognize  the  parts  of 
these  several  truths  which  are  asserted  in  the  proposition  to 
be  identical.  We  do  this  by  analyzing  the  terms  of  the  first 
member,  that  God  is,  and  discovering  that  one  part  of  the 
notion  God,  is  providential  ruler. 

To  illustrate  these  Rules  in  a  Hypothetical  proceeding  in 
the  relation  of  Part  and  Complementary  Part :  If  virtue 
is  voluntary,  vice  is  voluntary.  First,  we  recognize  the 
proposition  as  meaning  that  The  truth  that  virtue  is  volun- 
tary, involves  in  it  the  truth  that  vice  is  voluntary.  Next, 
we  recognize  those  parts  in  the  members  which  are  identical. 
The  attribute  of  morality  belongs  alike  to  virtue  and  vice,  as 
parts  complementary  of  each  other.  In  that  respect  they  are 
the  same  —  they  are  both  moral. 

It  will  have  been  observed  that  the  Hypothetical  Judg- 
ment occurs  often  in  discourse  as  a  true  reasoning,  as  a  kind 
of  Enthymeme,  one  of  the  premises  being  suppressed.  The 
terms  of  the  Judgment,  in  fact,  stand  in  the  relation  to  each 
other  of  a  conclusion  to  a  premise  ;  and  they  are  hence  ap- 
propriately called  respectively  the  Antecedent  and  Conse- 
quent members  of  the  Judgment. 


METHODOLOGY  OF  JUDGMENTS.        155 

§  93.  The  Fifth  distinction  of  Judgments  is  into  Extensive 
and  Comprehensive  or  Intensive  Judgments,  being   Ru]es  of 
founded  on   the   Logical  Quantity  of  their  terms.   f„  !^ent! 
The  conditions  of  a  perfect  Judgment  given  by  L°sical 

.       T       .  ~  Wholes. 

this  distinction  is  that  its  Logical  Quantity  be  dis- 
tinctly apprehended,  so  that  it  be  recognized  whether  the 
subject  or  the  predicate  is  the  containing  whole.  This  can 
always  be  effected  by  changing  the  form  of  the  Judgment  so 
as  to  put  it  into  the  phraseology  distinctive  of  the  two  Quan- 
tities. Thus  the  proposition,  Man  is  rational,  expressed  in 
Comprehensive  Quantity,  would  read  :  The  whole,  man,  con- 
tains in  its  complement  of  attributes  the  part  or  attribute 
rational.  In  Extensive  Quantity  :  The  part  or  species,  man, 
is  contained  under  the  whole  or  genus,  rational. 

§  94.  The  sixth  distinction  of  Judgments  is  founded  on 
the  kind  of  Whole  that  is  thought  in  the  matter  ?"les  of  ± 

°  Judgments 

of  the  Judgment,  whether  an  Integrate,  a  Substan-  indifferent 

•     1  ^  i    -rrr,       i  Wholes  of 

tial,  or  a  Causal  Whole.  Matter. 

This  distinction  imposes  this  condition  of  a  perfect  Judg- 
ment :  that  the  kind  of  Whole  expressed  by  the  terms  be 
clearly  recognized,  whether  an  Integrate  Whole,  the  parts 
of  which  lie  out  of  each  other;  or  a  Substantial  Whole,  the 
parts  of  which  permeate  each  other  as  simply  congruent ;  or 
a  Causal  Whole,  the  parts  of  which  permeate  each  other,  not 
only  as  congruent,  but  also  as  determined  through  the  same 
Causal  Whole.  Thus  Parts  in  a  Mathematical  Whole  are 
Parts  of  that  Whole ;  Parts  in  a  Substantial  Whole  are 
Parts  in  or  under  that  Whole,  according  as  the  Whole  is  a 
Comprehensive  or  Extensive  Whole ;  Parts  of  a  Causal 
Whole  are  Parts  through  that  Whole.  In  the  Mathematical 
or  Integrate  Whole,  the  nexus  is  simply  aggregation  ;  in  a 
Substantial  Whole,  the  nexus  is  substance ;  in  a  Causal 
Whole,  it  is  cause. 

§  95.  To  recapitulate  the  conditions  of  a  Perfect  Proposi- 
tion, that  is,  of  a  true  Judgment  truly  expressed,  it  is  neces- 
sary to  recognize  it  — 


156  PURE  LOGIC. 

1°.  As  to  its  Verbal  Form,  as  having  perfect  correspondence 
between  the  Thought  and  the  words. 

2°.  As  to  its  Quality,  whether  Identifying,  or  Differencing, 
or  Disjoining  in  contradictory  or  in  contrary  opposition. 

3°.  As  to  its  Modality,  whether  simply  Assertory,  or  Prob- 
lematic, or  Necessary. 

4°.  As  to  degree  of  its  Identification,  whether  Total  or 
Partial,  and  if  Partial,  in  respect  of  what  part. 

5°.  As  to  the  logical  Gradation  of  its  terms,  whether  Judg- 
ments, Concepts,  or  Integrate  Wholes ;  in  other  words, 
whether  Hypothetical  or  Categorical. 

6°.  As  to  the  logical  Quantity  of  its  Terms,  whether  if 
Logical,  an  Extensive  or  an  Intensive  Whole  ;  or,  if  Mate- 
rial, whether  an  Integrate,  a  Substantial,  or  a  Causal  Whole. 


CHAPTER  III. 

METHODOLOGY   OF   CONCEPTS. 

§  96.  The  Perfection  of  a  Concept  as  a  Synthesis  of  the 
homologous  terms  of  two  or  more  Judgments  iden-   The  three 
tified  through  the  sameness  of  the  other  term,  in-   0f  Perfection 
volves  three  conditions,  corresponding  respectively   m  e°ncePts- 
with  the  three  fundamental  virtues  of  perfect  science. 

The  first  condition  is,  that  the  terms,  which  being  combined 
form  the  concept,  be  the  homologous  terms  of  Judgments  hav- 
ing their  other  terms  the  same.  This  is  the  Objective  Law 
of  the  Concept,  giving  it  its  Material  Perfection. 

The  second  condition  is,  that  the  concept  itself  be  thought 
in  its  perfectness  as  a  "Whole  in  its  relations  both  to  other 
Concepts  and  to  its  Parts.  This  is  the  Subjective  Law  of  a 
Concept,  giving  it  its  Formal  Perfection. 

The  third  condition  is,  that  the  verbal  body  of  the  Concept 
truly  represent  the  matter  as  thought  in  it.  This  is  the 
Verbal  Law  of  a  Concept,  giving  it  its  Verbal  Perfection. 

§  97.  The  Objective  Law  of  the  Concept  enjoins  two  things : 

1°.  That  the  terms  combined  to  form  the  Con-  m    ... .  , 

The  Object- 

cept  be  recognized  as  homologous  terms.  ire  Law  of  a 

r  °  .  Concept. 

2°.  That  these    terms   be  recognized   as   from 
Judgments  having  the  other  terms  the  same  —  that  is,  that 
the  Base  be  recognized. 

The  validity  and  binding  force  of  these  two  rules  will  be 
recognized  at  once,  as  they  are  seen  to  be  but  the  applica- 
tion of  the  principle  of  Identity,  or,  as  it  is  in  this  relation 
denominated,  the  Law  of  Congruence,  to  Concepts. 

The  terms  united  to  form  the  Concept  must  be  homologous ; 


158  PURE  LOGIC. 

—  that  is,  must  be  either  all  subjects  or  all  predicates.  To 
attempt  tbe  union  of  subjects  with  predicates  in  the  same 
notion,  would  be  to  attempt  the  union  of  things  unlike  in 
respect  of  the  same  relation  in  which  they  are  to  stand  in  the 
union  —  to  identify  non-identities,  or  opposites. 

Further,  it  is  plain  that  not  all  homologous  terms  can  be 
synthesized  into  a  concept.  The  principle  of  Identity  that 
governs  all  thought  requires  that  the  terms  be  related  to  one 
another  by  having  a  common  element  for  each  of  the  other 
terms  of  the  primitive  Judgments,  which  common  element  we 
have  called  the  Base  of  the  Concept.  Thus  if  the  Concept  be 
in  Extensive  Quantity,  the  subjects  must  be  all  identified  in 
the  Judgments  with  the  same  predicate,  as  its  Base.  If,  on  the 
other  hand,  the  concept  be  one  in  Comprehensive  Quantity, 
the  predicates  which  compose  it  must  be  all  identified  in 
previous  Judgments  with  the  same  subject,  as  its  proper 
Base. 

It  is  to  be  observed,  moreover,  that  in  Thought  a  term  is 
not  the  same  unless  it  be  thought  in  the  same  kind  of  Whole. 
"We  may  suppose  terms  which  can  be  identified  in  Judgments 
with  the  same  subject  or  the  same  predicate,  but  in  different 
kinds  of  whole  ;  they  cannot  be  synthesized  into  a  Concept 
any  more  than  solids  and  surfaces.  Thus  we  have  as  true 
Judgments :  Man  is  biped ;  Man  is  soul  and  body ;  Man 
thinks  ;  but  the  incongruence  in  the  kinds  of  Wholes  in  which 
the  thought  moves,  forbids  the  synthesis  of  the  predicates 
into  a  Concept. 

In  order,  therefore,  to  the  more  thorough-going  determina- 
tion of  the  question  whether  two  given  terms  are  congruent 
or  not,  the  kind  of  whole  to  which  the  concept  belongs 
should  be  carefully  distinguished.  In  a  Mathematical  or  In- 
tegrate Whole,  the  parts  of  which  lie  out  of  each  other,  in- 
congruent  parts  are,  of  course,  only  such  as  overlap  each 
other.  Circles  and  rectilineal  figures  cannot  thus  be  united 
in  thought  as  making  up  any  polygon,  for  they  must  overlap 
each  other.     They  are  incongruent  parts.     Head  and  Bones 


METHODOLOGY  OF  CONCEPTS.  159 

are  incongruent  parts  of  Body ;  Fiber  and  Leaf,  of  Plant ; 
Thought  and  Predicate,  of  a  Sentence  ;  Sanction  and  Pro- 
mulgation, of  Law.  These  several  Wholes,  conceived  as  In- 
tegrate Wholes,  are  not  made  up  of  such  kinds  of  Parts  as 
appear  in  each  of  these  pairs.  The  parts  in  each  couplet 
overlap  each  other.  Thus  a  circle  may  be  contained  in  a 
polygon  ;  but  its  complement,  the  part  or  parts  which  with  the 
circle  make  up  the  polygon,  cannot  be  rectilinear.  Head  is 
a  part  of  Body  regarded  as  an  Integrate  Whole  ;  but  Bones 
are  not  the  complement  of  Head,  nor  do  they  with  any  other 
part  make  up  such  complement.  And  a  similar  view  must 
be  taken  of  the  other  examples.  The  parts  are  not  comple- 
mentary of  each  other.  They  are,  in  reference  to  the  same 
Whole,  incongruent,  inasmuch  as  in  any  attempt  to  fill  out 
the  given  whole,  some  part  must  overlap  some  other. 

In  a  Substantial  Whole,  in  which  the  Parts  permeate  each 
other,  the  incongruence  will  lie  in  the  opposite  nature  of  the 
Qualities  that  are  ascribed  to  the  Subject ;  or,  inasmuch  as 
a  Relative  Whole  may  be  represented  in  Thought  under  the 
analogies  of  a  Substantial  Whole,  in  the  opposite  nature  of 
the  Relations  ascribed  to  the  Subject.  Thus,  Blue  and  Red; 
Round  and  Angular  ;  Rough  and  Smooth  ;  Stiff  and  Flex- 
ible; Thick  and  Thin;  Skillful  and  Indolent;  Moral  and 
Deceitful,  are  respectively  pairs  of  Opposite  Incongruent 
Parts.  So  far  as  they  creep  into  the  same  Thought,  the  union 
is  fatal  to  the  Thought. 

In  a  Causal  Whole,  the  incongruence  will  lie  in  the  union 
of  parts  which  are  not  determined  by  the  same  cause.  The 
distinctive  relationship  of  the  parts  in  these  several  wholes 
as  before  observed,  is,  to  some  extent,  indicated  in  the  prepo- 
sitions that  are  commonly  used  to  express  it.  In  an  Integrate 
Whole,  the  parts  are  parts  of  the  whole ;  in  a  Substantial 
Whole,  they  are  in  or  under  the  whole  ;  in  a  Causal  Whole, 
they  are  through  the  whole.  Thus  Integrant  Parts  of  the 
notion  Man,  are  Body  and  Limbs;  Substantial  Parts  are 
Rational  and  Animal;  Causal  Parts  are  Virtue  and  Vice. 


160  JPURE  LOGIC. 

All  the  effects  which  may  be  through  the  cause  are  proper 
parts  of  a  Causal  Whole,  as  all  the  properties  which  are  con- 
tained in  an  object  conceived  as  Substance,  are  proper  parts 
of  that  substance.  Man,  thus,  as  Free  cause,  that  is,  Moral, 
contains  virtue  and  vice  through  this  freedom.  These  are 
Congruent  Parts  of  the  Causal  Whole,  Man  as  Moral ;  Incon- 
giuent  Parts  would  be  Virtue,  Vice,  Suffering.  So  of  the 
notion  Sculptor  as  cause,  Incongruent  Parts  would  be  Statiir 
ary,  Relief,  Carving,  Mosaic,  the  last  being  not  through  a 
Sculptor  as  such. 

It  might  be  thought  that  the  Objective  Law  of  the  Con- 
cept, as  thus  interpreted,  would  not  be  adequate  to  secure  in 
full  the  Material  Perfection  which  it  proposes.  But  in 
6trict  logical  consideration,  the  matter  of  a  Concept  is  given 
in  the  Judgments  from  which  it  is  derived  ;  and  consequently, 
the  law  of  its  formation  cannot  be  expected  to  go  back  of 
the  Judgments  which  are  its  proper  matter.  The  question 
whether  our  concept?,  which  make  up,  as  we  have  seen,  the 
great  body  of  our  notion-words  in  discourse,  do  actually  an- 
swer to  the  external  realities  to  which  we  unconsciously  in 
speaking  and  thinking  refer  them,  is  one  indeed  of  momen- 
tous concernment  to  us.  Are  these  notions  which  we  fabricate 
so  freely  in  our  thought,  all  unreal,  having  no  correspond- 
ences in  the  world  of  being  around  us  ;  are  our  references 
of  them  to  this  objective  world  all  illusory  and  deceptive ; 
or,  on  the  other  hand,  is  the  outer  world  constituted  on  the 
same  principle  of  Identity  which  underlies  and  governs  all 
Thought,  having  its  likes  and  its  unlikes,  its  samenesses  and 
its  differences  in  infinite  variety  and  extent,  exactly  an- 
swering to  the  infinite  variety  and  extent  of  our  Thought- 
products  —  is  the  universe  around  us  resolvable  into  the  self- 
same species  and  classes  which  appear  in  our  concepts,  so 
that,  if  our  thinking  be  legitimate,  we  may  rest  assured  that 
there  are  corresponding  species  and  classes  of  tilings  about 
us?  —  these  are  questions,  indeed,  of  most  vital  interest  to 
us  ;  but  they  lie  properly  out  of  the  domain  of  Pure  Logic. 


METHODOLOGY  OF  CONCEPTS.  161 

Yet  two  observations  may  without  impropriety  be  introduced 
here. 

First,  the  forming  of  Concepts,  as,  for  instance,  the  gather- 
ing into  classes  is  determined  by  the  special  occasion  or  object 
of  our  thinking.     Logic  does  not  prescribe  tbat,  any  more 
than  does  Arithmetic  prescribe  to  what  object  we  shall  apply 
its  processes  —  to  the  calculation  of  Interest,  or  the  compu- 
tation of   Magnitudes.     Logic    only   prescribes    the    proper 
movements  of  Thought,  when  Thought  is  required  for  any 
work  to  which  it  is  fitted.     We  must  not  then  expect  that 
the  outer  world  of  realities  should  be  broken  up  into  pre- 
cisely such  parts  as  the  occasions  of  our  thought  may  happen 
to  require.     In  other  words,  we  must  not  expect  that  the 
lines  of  separation  in  the  various  objects  of  the  actual  world 
are  distinctly  drawn  just  where  the  uses  of  our  thought  may 
lead  it  to  draw  them,  —  that  there  are  so  many  classes  of 
animals  or  vegetables  or  minerals  in  the  universe  as  we  may 
in  legitimate  Thought  choose  to  enumerate.     Classifications, 
Concepts,  vary  with  the  occasions  of  our  thinking,  with  the 
advancement  of  Science;  the  world  around  is   constant  in 
the  relationships  of  its  multiform  contents.     Generalizations 
in  Science,  thus,  will   sometimes   be   founded   on  essential 
attributes,   sometimes    on   extrinsic  attributes  or   relations ; 
sometimes  on  one  of  these  essential  attributes,  or  of  these 
relations,  sometimes  on  another.     Even  systems  of  natural 
science  will  vary,  in  respect  of  the  principle  of  classification 
and  consequently  in  respect  of  the  entire  method  of  the  par- 
ticular system,  with  the  advancements  of  the  science.     Ac- 
cepting the  doctrine  that  classification  in  the  science  of  nature 
must  be,  "  so  far  as  it  is  accurate,  the  literal  interpreter  of 
the  creative  plan  of  God," 1  and  must  rest,  therefore,  on  in- 
trinsic or  essential  attributes,  —  as  those  of  proper  Quality  as 
in  plan  of  structure  for  higher  classifications,  and  of  those  of 
Quantity  as  in  complicity  of  plan  for  lower,  —  we  yet  see  that 
even  here  there  is  room  for  much  diversity  among  naturalists 

»  L.  Agassiz,  Methods  of  Study  in  Natural  History,  chap.  iv. 
11 


162  PURE  LOGIC. 

in  their  perfectly  logical  systems  of  generic  arrangement, 
until  science  reaches  its  ultimate  limit.  "  The  plan  of  God 
in  creation  as  expressed  in  organic  forms  "  has  remained  the 
same  unchanged  through  the  successive  systems  of  Aristotle, 
Linnaeus,  Cuvier,  Baer,  and  their  co-workers  in  this  great 
field  of  science,  and  will  abide  the  same  through  all  the 
changing  systems  of  classification  as  they  go  on  in  the  ever- 
advancing  progress  to  a  perfect  science  which  shall  be  founded 
on  an  accurate  apprehension  of  all  the  facts,  and  a  congruent 
representation  of  them  in  forms  of  classified  knowledge,  con- 
venient for  the  uses  of  man  in  his  perfected  nature  and 
condition. 

Secondly,  that  there  is  a  true  correspondence  between 
legitimate  Thought  and  the  universe  of  Being  with  which  it 
is  conversant,  it  is  most  irrational  to  question.  Even  if  there 
be  not,  it  is  to  us  just  as  if  there  were ;  and  therefore  it  is 
unreasonable  to  call  the  correspondence  in  question.  Fur- 
ther, it  can  never  be  proved  that  there  is  no  correspondence  ; 
for  thought  is  impossible  where  there  are  no  .relations  —  no 
correspondences.  To  presume  such  want  of  correspondence 
so  as  to  throw  the  burden  of  proof  upon  the  party  that  af- 
firms the  correspondence,  is  but  most  unjustifiable  arrogation 
—  the  presumption,  whatever  there  may  be,  being  all  on  the 
other  side,  so  that  the  skeptic  must  be  held  to  make  good  his 
doubt,  that  is,  must  invalidate  his  own  skepticism.  Still 
further,  reason  and  revelation  agree  in  teaching  that  legiti- 
mate thought  has  its  counterpart  in  the  realities  of  its  objects. 
Reason  postulates  one  universe,  one  Creator,  one  principle 
of  creation  —  unity  in  the  wondrous  diversity,  harmony  in 
the  infinity  of  parts,  sameness  in  endless  difference ;  and  so 
we  are  taught  every  created  thing  is  created  "  after  his  kind." 
This  principle  of  kind,  of  identity  in  creation,  stamped  upon 
it  at  its  origin,  and  maintained  ever  by  the  same  Divine 
agency,  never  contradicting  itself,  that  first  brought  it  into 
being,  is  the  fundamental  principle  in  the  universe  of  things, 
exactly  answering  to  Thought.     There  is   a  true  kind,  a 


METHODOLOGY   OF   CONCEPTS.  163 

species  in  things,  that  never  perishes,  forbidding  transforma- 
tion into  other  kinds,  and  commingling  of  kinds,  so  that  if 
such  appear,  we  instinctively  and  truly  recognize  tliem  as 
monstrosities,  prodigies,  which  we  forbear  to  account  for  till 
we  attain  a  higher  point  of  view  from  which  to  look  out  on 
the  orderly  arrangement  of  things  that  appear  around  us  — 
a  higher,  purer  light  in  which  to  study  the  well-ordered 
universe  of  God.  Language,  in  its  various  forms,  as  shaped 
by  the  most  cultivated  portions  of  the  human  race,  attests 
the  general  acquiescence  of  men  in  the  correlativeness  of 
thought  and  specific  identity  in  nature.  The  words  genus, 
hind,  kin,  can,  know,  and  numerous  others,  all  of  one  stock, 
and  similar  in  the  different  dialects  of  the  great  Indo-Euro- 
pean family,  connect  causative  power,  intelligence,  and  specific 
identity  in  clearest  and  closest  relationship.  Things  are  alike 
because  the  creatures  of  the  same  causative  power ;  things 
correspond  to  our  thoughts,  because  we  and  they  are  products 
of  the  same  power  and  all  are  akin  to  it.  In  this  are  grounded 
alike  the  necessary  outward  condition  of  all  science  and  the 
universal  instinct  of  science  in  man.  Without  this  corre- 
spondence between  Thought  and  Being,  science  is  an  empty 
form ;  and  the  innate  aspiration  for  science  is  a  cheat  and  a 
lie.  Accepting  this  correspondence  with  a  natural  and  over- 
powering faith,  man  through  the  identities  cognizable  and 
validated  in  thought  rises  surely  and  successfully  along  the 
identities  of  creation,  upward  into  the  unity  of  the  single 
creative  power  in  the  universe,  and  attains  perfect  science. 

§  98.  The  Subjective  Law  of  a  concept  respects  the 
thought  side,    as  the    objective   law  respects  the   The  Subject- 
object  side,  of    this   product  or    the    Identifying   Concept. 
Faculty.     It  prescribes  the  conditions  of  a  perfect  cognition 
in  a  concept  so  far  as  they  respect  the  thinking  subject. 

The  two  virtues  of  a  cognition  lying  in  the  nature  of 
Thought  itself,  are  Clearness  and  Distinctness  —  Clearness 
constituting  the  perfection  of  a  concept  regarded  as  one 
whole  in  relation  to  other  wholes ;  Distinctness  being  its  per- 


164  PURE  LOGIC. 

fection  regarded  in  relation  to  its  own  parts.  Inasmuch  as 
these  are  exhaustive  complementary  views  in  thought  of  a 
thought-cognition  —  as  we  can  take  no  third  view  of  it  be- 
yond  the  view  of  it  as  a  part  in  relation  to  other  comple- 
mentary parts,  and  the  view  of  it  as  a  whole  in  relation  to 
its  own  parts  —  these  are  the  only  two  virtues  which  constitute 
its  perfection  as  a  Thought. 

The  Subjective  Law  of  a  Concept,  accordingly,  enjoins  — 

1.  Clearness,  or  that  the  concept  be  recognized  as  distin- 
guished from  all  other  concepts. 

2.  Distinctness,  or  that  the  concept  be  recognized  as  to  the 
several  parts  of  which  it  is  composed. 

The  process  by  which  Clearness  is  attained  is  called  Defi- 
nition. 

That  by  which  Distinctness  is  attained  is  called  Analysis. 

"  To  Leibnitz  we  owe  the  precise  distinction  of  concepts 
into  clear  and  distinct,  and  from  him  is  borrowed  the  follow- 
ing illustration.  In  darkness,  the  complete  obscurity  of 
night,  we  see  nothing  —  there  is  no  perception,  no  discrimi- 
nation of  objects.  As  the  light  dawns,  the  obscurity  dimin- 
ishes ;  the  deep  and  uniform  sensation  of  darkness  is  modi- 
fied ;  we  are  conscious  of  a  change  ;  we  see  something,  but  are 
still  unable  to  distinguish  its  features ;  we  know  not  what 
it  is.  As  the  light  increases,  the  outlines  of  wholes  begin  to 
appear,  but  still  not  with  a  distinctness  sufficient  to  allow  us  to 
perceive  them  completely  ;  but  when  this  is  rendered  possible, 
by  the  rising  intensity  of  the  light,  we  are  then  said  to  see 
clearly.  We  then  recognize  mountains,  plains,  houses,  trees, 
animals,  etc.,  that  is,  we  discriminate  these  objects  as  wholes, 
as  unities,  from  each  other.  But  their  parts  —  the  manifold 
of  which  these  unities  are  the  sum  —  their  parts  still  lose 
themselves  in  each  other,  they  are  still  but  indistinctly  visi- 
ble. At  length,  when  the  daylight  has  fully  sprung,  we  are 
enabled  likewise  to  discriminate  their  parts ;  we  now  see  dis- 
tinctly what  lies  around  us.  But  still  we  see  as  yet  only  the 
wholes  which  lie  proximately  around  us,  and  of  these  only 


METHODOLOGY  OF  CONCEPTS.  165 

the  parts  which  possess  a  certain  size.  The  more  distant 
wholes,  and  the  smaller  parts  of  nearer  wholes,  are  still 
seen  by  us  only  in  their  conjoint  result,  only  as  they  concur 
in  making  up  that  whole  which  is  for  us  a  visible  minimum. 
Thus  it  is,  that  in  the  distant  forest,  or  on  the  distant  hill,  we 
perceive  a  green  surface  ;  but  we  see  not  the  several  leaves, 
which  in  the  one,  nor  the  several  blades  of  grass,  which  in 
the  other,  each  contributes  its  effect  to  produce  that  amount 
of  impression  which  our  consciousness  requires.  Thus  it  is, 
that  all  which  we  do  perceive  is  made  up  of  parts  which  we 
do  not  perceive,  and  consciousness  is  itself  a  complement  of 
impressions,  which  lie  beyond  its  apprehension.  Clearness 
and  distinctness  are  thus  only  relative.  For  between  the 
extreme  of  obscurity  and  the  extreme  of  distinctness,  there 
are  in  vision  an  infinity  of  intermediate  degrees.  Now,  the 
same  thing  occurs  in  thought.  For  we  may  either  be  con- 
scious only  of  the  concept  in  general,  or  we  may  also  be 
conscious  of  its  various  constituent  subjects  or  attributes,  or 
both  the  concept  and  its  parts  may  be  lost  in  themselves  to 
consciousness,  and  only  recognized  to  exist  by  effects  or  rela- 
tions which  indirectly  evidence  their  existence. 

"  The  perfection  of  a  notion  is  contained  in  two  degrees  or 
in  two  virtues,  viz  :   in  its  clearness    and   in  its   clearness 
distinctness  ;  and,  of  course,  the  opposite  vices  of  *°y  asbiQU" 
obscurity  and  indistinctness  afford  two  degrees  or   ConcePts- 
two  vices,  constituting  its  imperfection.     A  concept  is  said 
to  be  clear,  when  the  degree  of  consciousness  by  which  it  is 
accompanied  is  sufficient  to  discriminate  what  we  think  in  and 
through  it,  from  what  we  think  in  and  through  other  notions  ; 
whereas  if  the  degree  of  consciousness  be  so  remiss  that  this 
and  other  concepts  run  into  each  other,  in  that  case  the  no- 
tion is  said  to  be  obscure.     It  is  evident  that  clearness  and 
obscurity  admit  of  various  degrees,  each  being  capable  of 
almost  infinite   gradations,  according   as    the  object  of  the 
notion  is  discriminated  with  greater  or  less  vivacity  or  pre- 
cision from  the  objects  of  other  notions.     A  concept  is  ab- 


166  PURE  LOGIC. 

solutely  clear,  when  its  object  is  distinguished  from  all  other 
objects ;  a  concept  is  absolutely  obscure,  when  its  object  can 
be  distinguished  from  no  other  object.  But  it  is  only  the 
absolutely  clear  and  absolutely  obscure  which  stand  opposed 
as  contradictory  extremes  ;  for  the  same  notion  can  at  once 
be  relatively  or  comparatively  clear,  and  relatively  or  com- 
paratively obscure.  Absolutely  obscure  notions,  that  is,  con- 
cepts whose  objects  can  be  distinguished  from  nothing  else, 
exist  only  in  theory ;  an  absolutely  obscure  notion  being,  in 
fact,  no  notion  at  all.  For  it  is  of  the  very  essence  of  a 
concept,  that  its  object  should,  to  a  certain  degree  at  least,  be 
comprehended  in  its  peculiar,  consequently  in  its  distinguish- 
ing, characteristics.  But  on  the  other  hand,  of  notions  ab- 
solutely clear,  that  is,  notions  whose  objects  cannot  possibly 
be  confounded  with  aught  else,  whether  known  or  unknown 
—  of  such  notions  a  limited  intelligence  is  possessed  of  very 
few,  and,  consequently,  our  human  concepts  are,  properly, 
only  a  mixture  of  the  opposite  qualities  —  clear  or  obscure 
as  applied  to  them,  meaning  only  that  the  one  quality  or  the 
other  is  the  preponderant.  In  a  logical  relation,  the  illustra- 
tion of  notions  consists  in  the  raising  them  from  a  prepon- 
derant obscurity  to  a  preponderant  clearness,  or  from  a 
lower  degree  to  a  higher.  So  much  for  the  quality  of  clear- 
ness or  obscurity  considered  in  itself. 

"  But  a  Clear  concept  may  either  be  Distinct  or  Indistinct ; 
The  Distinct-  the  distinctness  and  indistinctness  of  concepts  are 
dMin°tness  therefore  to  be  considered  apart  from  their  clear- 
of  Concepts.    negs  an(j  obscurity. 

"  We  have  seen  that  a  concept  is  clear,  when  we  are  able 
to  recognize  it  as  different  from  other  concepts.  But  we  may 
discriminate  a  whole  from  other  wholes,  we  may  discriminate 
a  concept  from  other  concepts,  though  we  have  only  a  con- 
fused knowledge  of  the  parts  of  which  that  whole  or  of  the 
characters  of  which  that  concept  is  made  up.  This  may  be 
illustrated  by  the  analogy  of  our  Perceptive  and  Representa- 
tive Faculties.     We  are  all  acquainted  with  many,  say  a 


METHODOLOGY  OF  CONCEPTS.  167 

thousand  individuals  ;  that  is,  we  recognize  such  and  such  a 
countenance  as  the  countenance  of  John,  and  as  not  the 
countenance  of  James,  Thomas,  Richard,  or  any  of  the  other 
nine  hundred  and  ninety-nine.  This  we  do  with  a  clear  and 
certain  knowledge.  But  the  countenances,  which  we  thus 
distinguish  from  each  other,  are,  each  of  them,  a  complement 
made  up  of  a  great  number  of  separate  traits  or  features ; 
and  it  might,  at  first  view,  be  supposed  that,  as  a  whole  is 
only  the  sum  of  its  parts,  a  clear  cognition  of  a  whole  coun- 
tenance can  only  be  realized  through  a  distinct  knowledge  of 
each  of  its  constituent  features.  But  the  slightest  considera- 
tion will  prove  that  this  is  not  the  case.  For  how  few  of  us 
are  able  to  say  of  any,  the  most  familiar  face,  what  are  the 
particular  traits  which  go  to  form  the  general  result ;  and  yet, 
on  that  account,  we  hesitate  neither  in  regard  to  our  own 
knowledge  of  an  individual,  nor  in  regard  to  the  knowledge 
possessed  by  others. 

"  Continuing  our  illustrations  from  the  human  countenance  : 
we  all  have  a  clear  knowledge  of  any  face  which  we  have 
seen,  but  few  of  us  have  distinct  knowledge  even  of  those 
with  which  we  are  familiar ;  but  the  painter  who,  having 
looked  upon  a  countenance,  can  retire  and  reproduce  its  like- 
ness in  detail,  has  necessarily  both  a  clear  and  distinct  knowl- 
edge of  it.  Now,  what  is  thus  the  case  with  perceptions  and 
representations,  is  equally  the  case  with  notions.  We  may 
be  able  clearly  to  discriminate  one  concept  from  another, 
although  the  degree  of  consciousness  does  not  enable  us  dis- 
tinctly to  discriminate  the  various  component  characters  of 
either  concept  from  each  other.  The  Clearness  and  Distinct- 
ness of  a  notion  are  thus  not  the  same;  the  former  involves 
merely  the  power  of  distinguishing  the  total  objects  of  our 
notions  from  each  other ;  the  latter  involves  the  power  of 
distinguishing  the  several  subjects,  the  several  attributes,  of 
which  that  notion  is  the  sum.  In  the  former  the  unity,  in 
the  latter  the  multiplicity,  of  the  notion  is  called  into  relief." 

§  99.  The  term  Definition  is  used  in  a  wider  and  looser,  or 


168  PURE  LOGIC. 

in  a  narrower  and  stricter  sense.  The  general  process  it- 
Definition-  se^  vvmch  it  denotes,  as  applied  to  various  objects, 
its  kinds.       js  ajso  variously  modified. 

As  the  object  of  all  definition  is  clearness,  which  is  a  qual- 
ity variable  in  degree,  the  term  definition  is  naturally  em- 
ployed to  denote  processes  that  imply  more  or  less  clearness, 
from  its  lowest  degree  in  mere  indication,  when  by  any  pecul- 
iarity whatever,  even  of  the  most  accidental  kind,  we  sep- 
arate one  object  from  another  in  our  view  of  it,  up  to  com- 
plete logical  definition,  which  entirely  bounds  out  the  object. 
The  process,  again,  may  be  applied  to  words,  to  concepts,  or 
to  any  cognition  of  the  Presentative  Faculties,  viewed  in  the 
relation  of  Whole  and  Part.  As  applied  to  words,  the  proc- 
ess is  called  Verbal  or  Nominal  Definition.  This  is  effected 
either  by  synonymous  words  or  expressions,  or  by  indicating 
the  etymology  of  the  term  to  be  defined.  The  term  concept, 
thus  is  defined  synonymously  as  a  notion,  and  etymologic- 
ally  as  that  in  thought  which  is  taken  with  something  else  ; 
breakfast  as  morning-meal,  or  as  that  by  which  we  break  fast ; 
definition  as  dilucidation,  or  as  the  act  of  bounding  or  limit- 
ing off. 

As  applied  to  concepts  and  carried  out  to  completeness  in 
order  to  perfect  science,  it  is  called  Logical  Definition. 

As  applied  to  cognitions  other  than  concepts,  it  is  called 
variously  Dilucidation,  Description,  or  Definition,  with  or 
without  modifying  words. 

In  its  application  to  an  Integrate  Whole,  we  have  exempli- 
fications of  its  use  in  Mathematical  Definitions  ;  as  a  Sector 
is  mathematically  defined  to  be  a  portion  of  a  circle  bounded  by 
two  radii  and  the  arc  interrupted  between  them.  Such  defini- 
tions have  the  completeness  of  a  proper  logical  definition. 
They  completely  separate  the  object  from  its  complementary 
part.  An  approximation  to  this  logical  completeness  is  at- 
tained in  the  definition  of  the  Fore-arm,  thought  as  part  of 
an  Integrate  Whole,  as  that  part  of  the  human  body  bounded 
by  the  wrist  and  the  elbow.  More  vaguely  and  incompletely 
is  Head  defined  as  the  upper  portion  of  the  body. 


METHODOLOGY   OF   CONCEPTS.  169 

In  its  application  to  Substantial  Wholes,  when  the  differen- 
cing element  must  be  found  in  an  attribute  by  which  it  is  dis- 
tinguished from  other  substances,  it  may  be  exemplified  by 
the  definition  of  man  as  substance,  that  is,  rational  animal  — 
a  definition,  as  will  be  seen,  that  corresponds  with  the  process 
in  a  proper  logical  whole.  The  only  difference  is,  that  here 
the  defining  members,  rational  animal,  are  viewed  as  real, 
not  as  thought,  attributes.  Parts  of  a  Substantial  Whole,  that 
is,  attributes,  may  be  defined  by  differencing  them  from  com- 
plementary attributes  of  the  same  substance. 

In  its  application  to  a  primitive  cognition,  viewed  as  a 
Causal  Whole,  definition  is  the  separation  of  one  cause  from 
other  causes  by  a  differencing  effect,  or  of  one  effect  from  the 
complementary  effect  of  the  same  cause.  Thus,  heating  is 
defined  as  the  effect  of  the  Sun  in  expanding  bodies  ;  expand- 
ing being  the  effect  which  differences  heat  from  other  causal 
agencies  of  the  sun. 

Logicians,  it  may  be  observed  here,  have  vaguely  distin- 
guished three  kinds  of  Definition  —  Verbal  or  Nominal,  Real, 
and  Genetic.  A  Verbal  Definition  is  the  elucidation,  the 
rendering  clear  of  the  term  or  object  through  its  name. 
Thus,  a  Verbal  or  Nominal  Definition  of  Concept  would  be, 
That  in  thought  which  is  taken  with  something  else.  A  Real 
Definition  of  Concept  would  be,  A  synthesis  of  the  homolo- 
gous terms  of  tivo  or  more  judgments  with  the  same  base. 
A  Genetic  Definition  would  be,  A  product  of  Thought  aris- 
ing from  the  synthesis  of  homologous  terms,  &c.  A  Verbal 
Definition  thus  elucidates  —  renders  clear  —  through  the 
Word;  a  Real  Definition  through  the  Substance;  a  Genetic 
Definition,  through  the  Cause  producing. 

§  100.  The  process  of  proper  Logical  Definition  consists  es- 
sentially in  recognizing  the  object  defined  as  a  part    ^ellSion- 
in  distinction  from  other  like  parts  of  a  larger  log-   its  nature. 
ical  whole  ;  that  is,  in  distinction  from  its  complementary  part. 

It  is  Extensive  or  Comprehensive  according  as   Definition 

1  °  either  Ex- 

the  concept  is  viewed  in  the  one  or  the  other  of    tensive  or 
these  kinds  of  Logical  Quantity.  sive. 


170  PURE  LOGIC. 

The  nature  and  validity  of  this  distinction  require  no  il- 
lustration. It  is  important  to  enounce  it  articulately,  that  in 
undertaking  the  process  of  definition  the  mind  may  move 
intelligently  and  freely.  As  the  same  name  is  ordinarily 
applied  in  Language  to  a  Concept  made  up  in  either  Quan- 
tity, it  becomes  the  more  necessary  to  determine  at  once  in 
denning  in  which  the  concept  is  to  be  viewed,  whether  as 
a  subject-concept  or  a  predicate-concept.  Definition  in  Ex- 
tension respects  the  subjects  of  which  the  concept  is  com- 
posed ;  Definition  in  Comprehension,  the  predicates  or  attri- 
butes. 

It  will  be  sufficient  to  exemplify  the  process  in  each  kind 
of  Quantity.  In  Extension,  then,  to  define  will  be  to  dis- 
criminate the  concept  from  all  coordinate  concepts ;  as  the 
whole  here  is  evidently  the  genus  made  up  of  the  concept  to 
be  defined,  and  the  coordinate  species.  We  attain  extensive 
clearness,  then,  in  a  'concept  of  a  right-angled  triangle  when 
we  discriminate  it  from  all  coordinate  triangles.  We  attain 
clearness  in  the  concept  man,  regarded  as  part  of  the  Ex- 
tensive whole,  animal,  when  we  discriminate  it  from  all  non- 
rational  animals  ;  in  the  concept  hope,  when  we  recognize  it 
as  complementary  of  fear,  in  the  class  of  emotions  called 
desires. 

In  a  Comprehensive  Whole,  clearness  is  attained  by  a 
recognition  of  that  character  or  that  complement  of  charac- 
ters in  the  concept  which  it  has  as  peculiar  to  itself,  and  not 
in  common  with  other  concepts.  Thus  we  attain  clearness 
in  the  concept  of  a  right-angled  triangle  in  comprehension, 
when  we  view  it  as  possessing  the  peculiar  property  of  having 
one  of  its  angles  right ;  of  man,  when  viewed  as  rational, 
and  thus  making  up  with  the  generic  property  of  a  brute,  the 
total  comprehension  of  rational  animal.  We  fasten  attention 
here  on  the  attribute ;  while  in  attaining  extensive  clearness 
we  look  at  the  subjects  of  which  the  attribute  is  predicated. 
As  for  the  most  part  terms  may  be  construed  in  either  quan- 
tity, the  results  attained  by  the  definition  will  so  far  be  ex- 
pressed in  similar  terms. 


METHODOLOGY  OF  CONCEPTS.  171 

The  examples  given  have  been  indiscriminately  in  contra- 
dictory and  in  contrary  opposition,  and  also  in  positive  and 
in  negative  characters.  The  strictest  logical  definition  will 
proceed  in  contradictory  opposition  —  accordingly  will  be 
dichotomous,  or  through  the  two  sections  of  Part  and  Com- 
plementary Part,  expressed  logically  as  A  and  non-A,  these 
two  contradictories  making  up  the  proper  whole  of  Thought. 
Plato's  definitions  are  characterized  as  of  this  form  —  dichot- 
omous or  bi-sectional,  proceeding  in  contradictory  opposi- 
tion. We  evidently  attain  strict  logical  clearness  when  we 
thus  discriminate  a  concept  from  its  complementary  part. 
Now,  as  in  the  case  of  any  concept  there  may  be  recognized 
many  kinds  of  parts  standing  in  this  relation  of  being  com- 
plementary to  it,  that  is,  as  making  up  with  it  so  many  kinds 
of  wholes,  it  is  obvious  there  may  be  as  many  perfect  defini- 
tions of  the  same  concept  as  there  are  different  kinds  of 
wholes  in  which  it  is  a  part.  Plato's  definition  of  man  as 
bird  without  feathers,  is  beyond  criticism,  if  the  whole  be 
taken  as  biped,  so  long  as  only  feathered  and  unfeathered 
beings  are  known  to  belong  to  this  class ;  for  it  discriminates 
perfectly  man  as  part  of  this  whole  from  its  complementary 
part.  The  so-called  Aristotelian  definition  of  man  as  an 
animal  walking  on  two  feet,  is  just  as  obnoxious  to  criticism 
as  Plato's,  and  no  more  so.  Howr  this  should  be  is  suffi- 
ciently shown  in  the  mode  of  forming  concepts,  if,  at  least, 
we  take  into  view,  also,  in  connection  with  this,  the  inade- 
quacy of  language  to  signalize  by  a  distinct  word  every  pos- 
sible synthesis  of  subjects  more  or  less,  or  of  predicates  more 
or  less,  on  any  Base  more  or  less  composite.  What  shall  be 
the  particular  whole  in  which  the  concept  to  be  defined  shall 
be  viewed,  and  consequently,  what  shall  be  the  definition, 
depends  then  on  the  occasions  of  use.  A  moral  philosopher 
would  define  man  in  one  way  ;  a  physiologist  in  another ; 
a  political  economist  in  a  still  different  way;  and  so  on, 
and  each  variously  on  the  varying  occasions  of  his  dis- 
course.    The  process  as  a  movement  of  Thought  remains 


172  PURE  LOGIC. 

ever  the  same  —  discrimination  as  part  from  the  comple- 
mentary part. 

But  as  such  movement  it  is  properly  in  its  first  step  only 
dichotomous,  or  by  discrimination  of  one  part  as  complement- 
ary. As,  however,  in  contrary  opposition  generally,  so  here 
the  thought  may  move  on  by  successive  definitions  in  the 
strict  Platonic  method,  till  we  attain  the  degree  of  clearness 
required.  Or  we  may  abridge  the  process  by  leaping  at  once 
to  the  results  of  such  continued  dichotomous  definition,  just 
as  the  arithmetician,  when  the  two  factors  of  seven  and  nine 
are  given,  leaps  to  the  product  sixty-three,  without  going 
through  the  entire  process,  step  by  step,  of  adding  seven 
units  to  other  seven,  and  seven  more  to  those,  and  so  on. 

Further,  we  may  define  indifferently  by  positive  or  by 
negative  characters,  as  we  may  discriminate  man  from  its 
complementary  part,  brute,  either  by  the  positive  character 
rational,  or  the  negative  character  not-brute  or  not-irra- 
tional. Evidently  what  is  positive  in  respect  of  one  part  is 
negative  in  respect  of  the  other  part.  The  movement  of 
Thought  is  indifferent  from  the  one  or  the  other,  and  the 
same  in  both.  The  occasions  of  discourse,  however,  gener- 
ally, and  of  preference,  demand  the  positive.  It  is  hence, 
from  the  occasions  of  discourse,  that  the  rule  springs  which 
prohibits  definition  by  negative  characters. 

The  convenient  and  logically  sound  rule  which  directs  us 
to  define  by  naming  the  next  higher  genus  and  the  specific 
difference,  has  the  recommendation  of  being  dichotomous, 
and,  by  an  easy  process  of  conversion,  of  being  explicable  in 
either  Quantity.  Thus  the  definition  of  man,  as  rational 
animal,  may  be  interpreted :  Man  is  of  the  genus  animal, 
and  the  species  rational ;  or,  Man  has  the  generic  attribute 
of  animal,  and  the  specific  attribute  of  rational.  Or  as  de- 
fined by  the  naturalist,  as  bi-manous  or  two-handed  mammal, 
it  may  mean :  of  the  genus  mammal,  and  species  bi-manous  ; 
or,  having  the  generic  character  of  mammal,  and  specific 
character  of  bi-manous.  Obviously,  however,  the  rule  has 
relation  only  to  proper  concept  wholes. 


METHODOLOGY   OF  CONCEPTS.  173 

§  101.  The  conditions  of  Distinctness  in  a  concept  are,  1. 
That  the  kind  of  parts  to  be  distinguished  be  first 
recognized ;  and,  2.  That  each  of  these  parts  be   its  Condi*38 
clearly  discriminated  from  the  other  parts. 

If  a  still  higher  degree  of  distinctness  is  required  than 
that  which  is  given  in  the  discrimination  of  the  first  set  of 
parts,  then  each  of  these  parts  may  be  treated  as  new  wholes, 
in  which  successively  distinctness  is  to  be  attained.  The 
process  will  be  the  same  as  in  distinguishing  the  first  set  of 
parts. 

Logical  Analysis,  then,  will  consist  of  the  two  processes, 
first,  of  recognizing  the  kind  of  parts  to  be  attained  in  the 
Analysis  ;  and,  secondly,  of  separating  into  these  parts.  The 
first  is  the  necessary  antecedent  condition  of  analysis  ;  the 
second  is  the  analysis  itself. 

§  102.  The  first  Law  of  Distinctness  requires  that  the 
kind  of  parts,  whether  Material  Parts,  as  Integrate,  Sub- 
stantial, or  Causal,  or  proper  Logical  Parts,  as  Extensive  or 
Comprehensive,  which  are  to  be  distinguished,  be  recognized. 
For  the  fuller  distinctness,  indeed,  the  parts  of  each  of  these 
kinds  may  be  discriminated.  Thus,  the  concept  Man,  may 
be  distinguished  into  the  Integrant  Parts  of  Head,  Body, 
and  Limbs  ;  or  into  the  Intensive  Parts  of  Rational  and 
Animal;  or  again  into  the  Extensive  Parts  of  Black, 
Tawny,  and  White;  or  the  Causal  Parts  of  Loving  and 
Hating.  But  in  any  case  the  kind  of  Parts  to  be  discrim- 
inated must  be  recognized.  The  necessity  of  this  Law  it  is 
unnecessary  further  to  illustrate. 

§  103.    The  particular  kind  of  parts  to  be  discriminated 
having  been  recognized,  the  next  step  is  to  effect   Analysis; 
the  distinction.      This  is  Proper  Analysis.      This   its  kiads' 
part   of   the    procedure  will    vary  with   the  kind  of   parts, 
giving  rise  to  so  many  subordinate  kinds  of  processes. 

That  process  by  which  Distinctness  is  attained  in  In- 
tegrant Parts  may  be  called  Dissection  ;  also,  Formal  Anal- 
ysis ; 


174  PURE  LOGIC. 

That  by  which.  Extensive  Parts  are  obtained  is  called 
Division  ; 

That  by  which  Intensive  Parts  are  obtained  is  called  Par- 
tition ; 

That  by  which  Causal  Parts  are  obtained  may  be  called 
Resolution;  also,  Evolution,  or  Causal  Analysis. 

It  will  not  escape  notice  that  one  kind  of  wholes  is  omitted 
in  this  enumeration  of  the  processes  of  analysis  —  that  of 
Substantial  Wholes.  The  reason  is,  that  while  the  ground 
of  distinction  exists,  yet  language  does  not  enable  us  to  dis- 
tinguish except  by  tedious  circumlocution  to  which  quick 
thought  and  speech  will  not  submit,  the  real  from  the  thought 
characters  of  an  object  of  thought  —  actual  properties  from 
thought  attributes.  We  should,  accordingly,  be  forced  to  use 
the  same  terms,  and  lay  out  the  same  rules  for  analysis  in 
Substantial  Wholes  as  for  analysis  in  Comprehensive  Wholes. 
With  this  intimation  of  the  reality  of  the  distinction,  and  of 
the  consequent  necessity  in  the  strictest  thought  of  observing 
it  on  supposable,  if  rare,  occasions,  to  avoid  perplexity, 
analysis  in  Substantial  Wholes  is  formally  omitted,  its  nature 
and  laws  being  readily  gathered  from  the  exposition  of  anal- 
ysis in  Comprehensive  Wholes. 

§  104.  There  is  one  general  Law  of  Analysis  applicable 
Law  of  Com-  to  all  the  subordinate  processes  alike.  It  is  the 
pieteness.  general  Law  of  Adequacy  appearing  here  in  the 
specific  form  of  the  Law  of  Completeness  requiring  that  all 
the  Parts  in  the  given  Analysis  be  recognized.  The  neces- 
sity of  this  is  obvious.  So  far  as  the  Analysis  is  incomplete 
some  one  or  more  parts  being  omitted  from  the  recognition, 
the  cognition  fails  in  distinctness.  Besides  this,  it  must  of 
necessity  be  partial  and  one-sided,  and  positive  error  will  be 
the  result.  For  example,  if  in  analyzing  Faith  as  a  Chris- 
tian virtue,  I  recognize  only  the  characters  of  Intellectual 
Belief,  and  Sentiment  of  the  Heart,  leaving  out  all  Moral 
Disposition,  Purpose,  or  Will,  I  make  it  a  merely  involun- 
tary state,  and,  of  course,  exclude  from  the  notion  all  free- 
dom, all  responsibility,  all  morality. 


METHODOLOGY  OF   CONCEPTS.  175 

The  practical  importance  of  a  careful  observance  of  this 
Law  of  Logical  Analysis  is  to  be  seen  in  the  fact  that  by  far 
the  greatest  part  of  erroneous  opinion  in  all  departments  of 
knowledge  arises  from  the  incomplete  apprehension  of  the 
objects  of  knowledge.  Most  dissensions  in  science  and  in 
belief  would  be  ended  by  a  complete  survey 'of  all  the  con- 
stituent elements  of  the  matter  in  dispute.  It  is  mainly  be- 
cause the  parties  look,  one  at  one  element,  the  other  at 
another,  and  each  to  the  exclusion  from  his  view  of  some 
element  or  character  important  to  a  correct  opinion,  that  any 
dissension  arises. 

§  105.  Passing  now  to  the  subordinate  processes  of  Log- 
ical Analysis,  the  first,  Formal  Analysis  or  Dis-  Dissection : 

J  .  .  its  two 

section,  is  that  which  gives  as  its  result  Integrate  kinds. 
Parts.  These  are  of  two  kinds  —  Spacial  and  Numerical. 
The  distinctive  characteristic  of  each  kind  is  that  the  parts 
lie  out  of  each  other.  The  fundamental  condition  of  a  cor- 
rect analysis  here,  accordingly,  being  that  no  part  overlap 
another,  we  have  the  comprehensive  Law  of  Formal  Analysis 
or  Logical  Dissection  that  it  proceed  from  a  single  principle  ; 
that,  for  instance,  but  one  point  of  departure  in  lineal,  one 
line  in  superficial,  one  plane  in  solid  dissection,  be  taken ; 
and  in  numerical  parts,  one  unit  of  separation.  Thus  in  dis- 
secting tree  regarded  in  simply  lineal  extent,  to  take,  as  one 
part,  that  below  the  ground,  and  as  another,  that  between 
the  branching  of  the  roots  and  the  branching  of  the  boughs, 
would  vitiate  the  process,  as  giving  parts  that  overlap  each 
other.  So  to  analyze  the  United  States  of  America  as  a 
spacial  extent  by  taking  the  Atlantic  States,  the  Pacific 
States,  the  Lake  States,  the  Gulf  States,  and  the  Mississippi 
Valley  States,  even  if  it  were  complete,  would  be  incorrect, 
for  the  lines  of  dissection  cross  each  other,  giving  overlap- 
ping parts.  So  to  dissect  hope  into  expectation,  desire,  and 
pleasure,  is  vicious,  inasmuch  as  pleasure  is  not  attained  by 
the  same  line  of  dissection  as  the  other  parts.  It  overlaps 
both. 


176  PURE  LOGIC. 

So  in  Numerical  Parts,  to  dissect  a  dollar  into  shillings 
and  dimes  would  necessarily  give  overlapping  parts  ;  or  to 
separate  solar  light  into  full  splendor,  cloudiness,  moon- 
light, and  twilight,  the  unit  of  Degree  of  Intensity  not  being 
apprehended,  the  parts  overlap  one  another ;  or  to  distin- 
guish merit  as  perfect,  average,  fair,  and  zero,  the  third  dis- 
tinction of  degree  not  corresponding  with  the  other  three. 

§  106.  The  second  kind  of  Logical  Analysis  is  that  of 

. .  Division,  which  gives,  as  its   proper  result,  the 

Extensive  Parts  of  a  Logical  Whole ;  —  in  other 
words,  the  objects  contained  under  the  whole  which  must 
here  ever  be  regarded  as  a  genus  or  class,  that  is,  a  subject- 
whole. 

The  first  step  in  Division  is  to  recognize  the  specific  kind 
of  parts  that  are  sought  in  the  Analysis.  From  the  very 
nature  of  a  subject-concept,  that  may  have  as  its  Base  a  plu- 
rality of  attributes,  there  may  be  as  many  modes  of  division, 
each  giving  its  own  set  of  parts,  as  there  are  different  attri- 
butes synthesized  in  the  Base.  Thus,  man  is  a  subject- 
concept  with  a  Base  of  the  two  intrinsic  attributes,  rational 
and  animal ;  and  the  concept  may  be  analyzed  into  rational 
parts,  as  cultivated  and  barbarous;  learned  and  unlearned; 
intellectual,  sentimental,  and  practical;  or  into  animal 
parts,  as  tall  and  short ;  white,  tawny,  and  black ;  sanguine 
and  bilious,  and  the  like.  The  concept  has  likewise  a  Base 
of  manifold  extrinsic  attributes,  or  attributes  of  Relation, 
which  will  furnish  so  many  other  modes  of  division  and 
sets  of  parts  ;  as  HJuropean,  Asiatic,  &c,  in  relation  to  coun- 
try or  place ;  antediluvian  and  post-diluvian ;  governors 
and  governed,  and  the  like.  An  analysis  that  should  pre- 
sent parts  of  these  various  kinds,  taken  indiscriminately  and 
confusedly,  would  obviously  be  of  no  worth,  as  it  would  be 
without  logical  method.  «We  must  then,  as  the  first  step  in 
division,  apprehend  the  attribute  in  the  Base  of  the  concept 
in  reference  to  which  the  analysis  is  to  be  made.  The  at- 
tribute selected  for  this  purpose  is  called  the  Principle  of 


METHODOLOGY  OF  CONCEPTS.  177 

Division.  Thus  the  Division  of  man  into  cultivated  and  bar- 
barous  has  for  its  principle  of  division  the  attribute  cultivated, 
being  comprehended  in  the  more  comprehensive  attribute 
rational ;  .that  of  man  into  white,  tawny,  and  black,  is  color, 
being  an  attribute  comprehended  in  animal.  A  Division, 
it  is  seen  thus,  is  effected  simply  by  adding  an  attribute 
to  the  Base  of  a  Subject-concept,  or  Extensive  Whole,  as  by 
adding  to  rational  animal  the  attribute  cultivated,  or  black, 
we  obtain  corresponding  divisions  of  the  concept  man. 

The  first  and  the  only  proper  logical  division  is  dichoto- 
mous ;  giving  the  two  parts,  one  having  the  attribute  which 
forms  the  principle  of  division,  the  other  not ;  as  man  is  of 
the  two  species,  cultivated  man  and  not  cultivated,  that  is, 
barbarous  man ;  angles  are  right  angles,  and  angles  that 
are  not  right.  But  generally  a  farther  division  is  required, 
and  in  the  enumeration  of  the  parts  those  that  are  negative 
are  not  specially  mentioned,  but  are  represented  in  the  sub- 
ordinate divisions.  Thus  instead  of  a  division  of  man  in 
respect  of  Color,  first  into  white  and  not  white,  and  then 
not  white  into  the  two  colored  species,  tawny  and  black, 
the  division  is  made  at  once  into  the  three  varieties  ;  and 
angles  are  divided  into  right,  acute,  and  obtuse.  The  three 
parts  thus  obtained  are  in  looser  language  denominated 
coordinate,  inasmuch  as  each  is  complementary  of  the  other 
two.  In  such  case  the  more  comprehensive  attribute  is  the 
principle  of  division  ;  as  color  and  magnitude  respectively 
in  the  examples  given.  In  the  same  way  there  may  be  any 
number  of  parts. 

The  first  thing,  then,  to  be  done,  in  effecting  division,  is  to 
recognize  the  principle  of  division,  or  the  attribute  in  respect 
of  which  the  division  is  made.  This  being  done,  the  one  law 
of  division  is  — 

That  all  the  coordinate,  that  is,  complementary  parts,  given 
by  the  principle  of  division,  and  none  others,  be  distin- 
guished. 

12 


178  PURE  LOGIC. 

This  comprehensive  Law  comprehends  the  following  par- 
ticulars :  — 

1°.  That  none  but  parts  —  individuals  or  species  —  con- 
tained under  the  given  Whole,  be  taken. 

2°.  That  no  objects  or  parts  be  taken  which  are  not 
strictly  coordinate  with  one  another  under  the  adopted  prin- 
ciple of  division. 

3°.  That  subordinate  objects  or  species  be  apprehended  as 
contained  under  the  super-ordinate. 

4°.  That  all  the  coordinate  species  be  distinguished. 

§  107.  The  third  kind  of  Logical  Analysis  is  that  of  Par- 
tition, which  gives  as  its  proper  result  the  Corn- 
Partition.  '.  °  . 

prehensive  Parts  of  a  Logical  Whole;  in  other 

words,  the  characters  or  properties,  inherent  or  relative,  that 
make  up  the  whole.  The  parts  in  this  species  of  whole 
permeate  each  other,  and  are  comprehended  in  the  whole. 

The  first  step  in  Partition  is  to  recognize  some  one  char- 
acter or  property  as  that  which  shall  determine  the  kind  or 
olass  of  properties  sought  in  the  Analysis.  What  that  char- 
acter shall  be  it  is  not  the  province  of  Logic  to  prescribe ; 
that  is  to  be  determined  by  the  object  proposed  in  the  Anal- 
ysis, the  consideration  of  which  belongs  to  Rhetoric  or  the 
Art  of  Discourse.  Logical  Science  cannot  discriminate  be- 
tween the  characters  or  properties  that  make  up  a  concept, 
as  to  their  relative  importance.  It  can  only  discriminate 
them  as  Intrinsic  or  Extrinsic  ;  as  Conflicting  or  Congruent ; 
as  Involving,  or  Involved,  or  Coordinate  ;  for  it  cannot  tran- 
scend the  relationship  of  Whole  and  Part. 

Some  one  particular  character  or  property  having  been 
thus  selected  which  shall  determine  the  set  of  characters  to 
be  taken  as  making  up  the  concept,  the  Law  of  the  Analysis 
itself  will  be  derived  from  the  indicated  relations  of  the 
character  to  the  Whole  and  to  the  other  characters.  This 
Law  is  — 

That  none  but  coordinate  characters,  and  all  of  them,  be 
distinguished. 


METHODOLOGY  OF  CONCEPTS.  179 

This  general  Law  contains  the  following  particulars  :  — 

1°.  That  none  but  actual  characters  be  taken. 

2°.  That  no  connective  characters  be  taken. 

3°.  That  involved  characters,  if  distinguished  at  all,  be 
apprehended  as  contained  in  the  involving  character. 

4°.  That  all  the  coordinate  characters  be  distinguished. 

§  108.  The  Fourth  kind  of  Logical  Analysis  is  that  of 
Resolution,    otherwise    called    Evolution    and  „    ,  „ 

,  Resolution. 

Causal  Analysis,  which  gives  as  its  proper  results 
the  Causal  Parts  ;  in  other  words,  effects  as  parts  of  the  con- 
cept viewed  as  Cause. 

The  first  step  here  is  to  recognize  the  kind  of  effects  into 
which  the  concept  is  to  be  resolved  by  apprehending  some 
one  effect,  which  with  all  the  others  shall  make  up  the  com- 
plement of  effects  through  that  Cause.  Here  it  should  be 
remembered  that,  from  the  imperfectness  of  Language,  the 
same  name  may  denote  Causes  of  widely  variant  effects. 
Thus  Man  is  a  name  of  a  Causal  agency  operating  in 
many  conceivable  different  spheres  ;  as,  for  instance,  mate- 
rially, as  counterpoising  more  or  less  weight ;  chemically,  as 
forming  by  decomposition,  nitrogen,  carbon,  and  other  chem- 
ical elements  ;  organically,  as  breathing,  digesting,  &c. ;  spir- 
itually, as  thinking,  desiring,  willing,  and  the  like.  The 
cause  in  counterpoising,  it  is  obvious,  is  not  the  same  as  in 
breathing,  or  in  thinking.  It  becomes  necessary  in  order  to 
Distinctness  in  a  Causal  Whole  to  apprehend  first  the  kind 
of  effects  which  constitute  it,  which  is  done  by  taking  some 
one  effect  as  the  determining  one  of  the  set  of  effects  to  be 
attained  in  the  Analysis. 

This  being  done,  the  Comprehensive  Law  of  Causal  Anal- 
ysis for  attaining  Distinctness  is  — 

That  none  but  coordinate  effects,  and  all  of  them,  be  dis- 
tinguished. 

This  Comprehensive  Law  comprises  the  following  partic- 
ulars :  — 

1°.  That  none  but  actual  effects  of  the  given  Cause  bo 
taken. 


180  PURE  LOGIC. 

2°.  That  no  effects  be  taken  which  are  not  strictly  coordi- 
nate with  one  another. 

3°.  That  derivative  effects  be  apprehended  as  contained 
through  the  original  effect  from  which  they  are  derived. 

4.°  That  all  the  coordinate  effects  be  distinguished. 

§  109.  The  Verbal  Law  of  a  concept  divides  itself  into 
two  parts,  one  determined  by  its  relation  to  the  Thought  ex- 
pressed in  it,  the  other  by  the  nature  of  verbal  expression. 

I.  The  Verbal  Law  of  a  concept  requires  that  the  Ex- 
pression be  exactly  conformed  to  the  Thought  to  be  expressed. 
This  involves  — 

1°.  That  the  Expression  contain  the  exact  Thought; 

2°.  That  it  contain  all  the  Thought ;  and  — 

3°.  That  it  contain  no  more  than  the  Thought. 

The  necessity  of  a  careful  observance  of  these  laws  rests 
chiefly  on  the  fact  that  Language  is  at  best  an  inadequate  ex- 
pression of  Thought.  It  furnishes  but  a  single  term  for  a 
great  multiplicity  of  thoughts.  Hence  the  necessity  of  choos- 
ing, in  the  first  place,  the  fittest  terms  for  expressing  the 
Concept  and  the  parts  contained  in  the  Analysis ;  and,  in 
the  second  place,  when  the  term  is  not  exactly  adequate  to 
the  Thought,  of  modifying  it  so  as  to  make  the  thought  and 
the  expression  exactly  coincident. 

One  application  of  this  part  of  the  general  Verbal  Law 
of  the  Concept  is  of  especial  interest  and  importance.  It 
respects  the  verbal  expression  of  the  quantity  of  the  concept. 
The  importance  of  a  distinct  recognition  of  this  application 
of  the  law  originates  in  the  fact  that  Language  ordinarily 
fails  to  distinguish  in  the  form  of  the  word  the  kind  of  quan- 
tity which  is  intended.  The  word  tree,  for  example,  may  be 
used  to  denote  an  Extensive,  an  Intensive,  or  an  Integrate 
Whole  ;  —  to  denote  a  class  of  objects,  a  complement  of 
attributes,  or  a  certain  individual  object.  When  such  words 
are  used  without  modifying  words  to  indicate  the  quantity, 
they  may  be  taken  in  either  one  of  these  several  meanings  ; 
and  when  they  are  repeated  in  the  same  general  movement 


METHODOLOGY  OF  CONCEPTS.  181 

of  thought  in  different  relations,  there  is  great  liability  to 
confusion  and  error,  which  can  be  detected,  perhaps,  only 
through  a  discrimination  of  these  several  kinds  of  quantity. 
Logicians  even,  for  a  single  exemplification,  have  often  failed 
to  recognize  the  difference  between  the  expression,  No  man 
is  immortal,  and  the  proper  negative  proposition,  Man  is 
not  immortal.  They  class  and  treat  them  both  as  alike  uni- 
versal negative  judgments.  But  there  is  a  most  material 
difference  in  the  import  of  the  two  propositions.  Man,  in 
the  first  proposition,  is  necessarily  to  be  construed  as  an  In- 
tegrate Whole ;  Avhile  man,  in  the  other  proposition,  is  a 
Class  Whole.  How  easily  error  may  creep  into  a  continuous 
movement  of  thought,  through  the  loose  employment  of 
words  of  this  kind,  may  be  seen  in  an  example  of  a  fallacious 
reasoning.  Thus  :  Man  is  not  philosopher  ;  Newton  was  a 
man  ;  therefore,  Newton  was  not  a  philosopher.  The  truth 
of  the  sumption,  interpreting  the  term  man  as  a  class  whole, 
is  unquestionable.  Equally  so  is  the  truth  of  the  subsump- 
tion.  Yet  the  reasoning  is  fallacious,  being,  in  fact,  an  in- 
stance of  that  kind  of  fallacy  to  be  explained  in  the  sequel, 
called  the  fallacy  of  four  terms.  Palpable  as  the  error  is 
here,  it  is  easy  to  see  that  in  the  progress  of  continuous  dis- 
cussion the  fallacy  might  readily  creep  in.  The  familiar 
rule  of  formal  logic  requiring  the  distribution  of  one  term  in 
a  reasoning  is  aimed,  in  part,  against  this  sophistry  in  some 
of  its  forms. 

II.  The  Verbal  Law  of  a  Concept  requires,  in  the  second 
place,  that  the  verbal  expression  conform  to  the  laws  of  ex- 
pression.    This  involves  — 

1°.  That  the  expression  be  significant. 

2°.  That  it  be  perspicuous. 

3°.  That  it  be  brief. 

The  first  of  these  particulars  prohibits  all  unmeaning 
terms,  all  needless  repetitions,  all  tautological  expressions. 
Significance  should  characterize  the  whole  and  every  part  of 
the  expression. 


182  PURE  LOGIC. 

The  second  prohibits  the  use  of  ambiguous,  obscure,  and 
figurative  terms ;  and  also  requires  such  a  structure  as  the 
settled  principles  of  language  impose  in  order  to  perspicuous- 
ness. 

The  third  prohibits  all  unnecessary  words,  and  also  peri- 
phrastic expressions  not  necessary  for  accuracy  and  ade- 
quateness. 


CHAPTER  IV. 

METHODOLOGY    OF   REASONINGS. 

§  110.  The  triform  perfection  of  Thought  generally,  Mate- 
rial, Formal,  and  Verbal,  requisite  to  perfect  science,  im- 
poses upon  the  Reasoning  process  as  a  derivation  from  one 
or  more  Judgments  the  three  Laws  which  we  have  distin- 
guished as  the  Objective,  the  Subjective,  and  the  Verbal. 
We  will  consider  the  application  of  these  Laws  to  the  differ- 
ent forms  of  Reasoning  under  each  Law  in  order. 

Before  entering  upon  this  consideration,  however,  it  is 
proper  to  recall  a  distinction  of  methods  already  pr0bation 
stated,  founded  on  the  different  ends  for  which  gondii-1" 
thought  is  exerted.  "We  have  distinguished  the  tingi^ed. 
two  ends  of  attaining  truth  and  of  communicating  truth  — 
here  appearing  specifically  as  those  of  Investigation  and 
Probation.  The  process  of  thought  in  the  two  methods  is  es- 
sentially the  same  ;  but  the  movement  is  generally  and  charac- 
teristically in  opposite  directions.  Thus,  in  attaining  truth, 
in  investigating,  we  begin  with  the  proper  logical  antecedent 
—  with  the  premises ;  while  in  communicating  truth,  in  pro- 
bation, we  ordinarily  begin  with  the  conclusion.  This  dif- 
ference, however,  is  not  one  of  strict  logical  concernment. 
The  movement  in  investigation  is  that  which  is  most  proper 
for  logical  consideration  ;  and  to  verify  thought  in  probation, 
the  doctrine  of  which  belongs  pi*operly  to  Rhetoric,  it  be- 
comes necessary,  therefore,  to  reverse  the  movement,  so  that 
the  conclusion,  which  in  argumentation  is  ordinarily  placed 
first,  shall  stand  in  its  true  logical  position  after  the  ante- 
cedent.    As  we  shall  see,  many  of  the  fallacies  ordinarily 


184  PURE    LOGIC. 

considered  in  systems  of  Logic,  being  purely  fallacies  of  pro- 
bation and  not  of  investigation,  belong  to  Rhetoric. 

It  may  be  added  here,  that  in  probation  the  thought  is 

generally  presented  but  in  part,  as  in  the  Enthymeme,  in 

which  one  premise  is  suppressed.     To  verify  the    thought, 

Logic  requires  that  it  be  filled  out  in  all  its  essential  parts. 

§  111.   The  Objective  Law  of  a  Reasoning 

Objective  .  .       ,  " 

Law  of         requires  that  the  Antecedent  be  distinctly  recog- 

Reasonings.  ..  .       „  .   . 

nized  as  to  its  iorm  and  import. 

The  Antecedent  in  a  Reasoning,  it  will  be  recollected,  is 
the  Judgment,  or  the  Judgments,  which  are  given,  from  which 
the  Consequent  or  Conclusion  is  to  be  thought  out  in  the 
Reasoning.  It  is  the  proper  matter  or  datum  in  the  process, 
and  must,  consequently,  in  order  to  perfect  science,  be  ac- 
curately and  adequately  apprehended. 

This  Law,  then,  presupposes  the  perfection  of  the  Judgment 
or  Judgments  which  form  the  Antecedent  as  the  datum  of 
the  Reasoning.  It  prescribes  as  additional  requisites  to  per- 
fect science  — 

1°.  That  the  Antecedent  be  recognized,  whether  as  Simple 
or  as  Composite,  that  is,  be  recognized  as  to  the  number  of 
Judgments  of  which  it  is  made  up. 

2°.  That  the  specific  character  of  each  Judgment  in  the 
Antecedent  be  recognized  in  its  Quality,  whether  Affirmative, 
Negative,  or  Disjunctive  ;  in  its  Modality,  whether  Assertory, 
Problematic,  or  Apodictic ;  in  its  Degree,  whether  Identical 
or  Partial ;  in  its  Form,  whether  Categorical  or  Hypotheti- 
cal ;  in  its  Logical  Quantity,  whether  Extensive  or  Compre- 
hensive ;  in  its  Material  Quantity,  whether  Integrate,  Sub- 
stantial, or  Causal. 

3°.  That  the  Verbal  Expression  be  recognized  as  correctly 
and  unequivocally  rendering  the  Thought,  and  in  a  form 
appropriate  to  the  Reasoning  process,  or  at  least  reducible  to 
such  form. 

The  logical  soundness  of  these  rules  it  would  be  superflu- 
ous to  vindicate  at  length  and  in  form ;  but  the  importance 


METHODOLOGY  OF  REASONINGS.  185 

of  forming  the  habit  of  thus  weighing  in  each  integral  part 
the  datum  of  a  reasoning,  can  hardly  be  overrated.  It  is 
only  necessary  to  add  that  while  it  is  not  difficult  to  form 
the  habit,  so  that  instinctively  and  unconsciously  as  it  were, 
the  precise  matter  of  the  reasoning  shall  be  so  fully  appre- 
hended as  to  bring  to  light  any  defect  or  ground  of  fallacy, 
this  can  be  only  by  a  conscious  separate  attention  at  first  to 
each  essential  part  of  the  Antecedent. 

The  applications  of  this  Law,  so  far  as  they  are  peculiar 
to  any  one  kind  of  reasoning,  will  be  considered  under  each 
one,  and  in  connection  with  its  Subjective  Law. 

§  112.  The  Subjective  Law  of  a  Reasoning  respects  the 
movement  of  Thought  itself  in  deriving;  the  con-   „  . .   „ 

°  °  Subjective 

elusion  or  consequent  from  the  Antecedent.       It   Law  of 

Reasonings. 

will  vary  under  its  more  general  twofold  form  in 
the  two  different  relations  of  Whole  to  Part,  and  of  Part  to 
Complementary  Part,  with  the  particular  kind  of  Reason- 
ing. We  will  accordingly  consider  the  Law  in  its  various 
forms  of  application  to  the  different  species  of  Reasoning  in 
order,  beginning  with  Immediate  Reasonings  in  their  several 
forms  of  Conversion,  Quantitative  Restriction,  Modal  Restric- 
tion, Transference,  Disjunction,  and  Composition ;  and  con- 
tinuing with  Mediate  Reasonings  in  their  several  species  of 
the  Syllogism,  Categorical  and  Conditional,  and  the  Polysyl- 
logism. 

Inasmuch,  however,  as  fallacious  thinking  generally,  if 
not  always,  is  occasioned  by  the  complication  of  divers  simple 
processes  in  one,  it  becomes  necessary  to  premise  one  gen- 
eral rule  of  high  importance  to  correct  thought. 

§  113.  In  every  case  of  the  intermingling  of  several  proc- 
esses of  Thought  in  the  same  general  movement,   „ 

°  to  '    Law  of 

the  attainment  of  assured  Truth  requires  that  each   Complex 

.  Thought. 

process  in  the  complex  thought  be  distinguished 
and  verified  through  its  entire  progress. 

No  perfectly  simple  process  of  thought,  perhaps,  even  with 
the  dullest  intelligence,  can  mislead  or  err.     It  is  only  when 


186  PURE  LOGIC. 

processes  are  blended  together  and  the  thonght  becomes  in- 
tricate that  error  or  fallacy  is  possible.  The  proper  and  the 
only  certain  and  universal  cure  is  the  separate  recognition 
and  verification  of  each  distinct  process  that  enters  into  the 
complex  movement. 

The  enunciation  of  this  general  Law  will  preclude  the 
necessity  of  multiplying  specific  rules  for  all  the  different 
kinds  of  complex  reasoning.  It  will  be  sufficient  here  to 
exemplify  the  Law  in  reference  to  these  complications  in  a 
very  general  way. 

Conversion  is  often  combined  with  Restriction,  whether  in 
Quantity  or  in  Modality,  and  also  with  Transference.  Logi- 
cians have  accordingly  distinguished  so  many  different  kinds 
of  Conversion  with  tabular  forms,  showing  when  inference  is 
possible,  when  not,  and  on  what  conditions,  with  as  much 
reason  for  any  practical  utility,  as  if  a  mathematician  should 
tabulate  all  the  possible  combinations  of  addition,  subtraction, 
multiplication,  and  division  in  any  arithmetical  process,  for 
directing  how  to  compute  in  each.  We  may,  indeed,  gener- 
alize the  statement,  by  enouncing  that  Immediate  Reasonings 
intermingle  in  all  possible  combinations,  not  only  with  one 
another,  but  also  with  Mediate  Reasonings  of  all  kinds,  sub- 
ject only  to  the  general  laws  of  Thought.  Examples  of  the 
former  kind  are  Conversion  per  accidens,  as,  Convertend,  A 
is  B ;  Converse,  some  B  is  A,  where  Conversion  is  com- 
bined with  Quantitative  Restriction  :  Conversion  by  Contra- 
position, as,  Convertend,  A  is  B ;  Converse,  no  Non-B  is  A, 
where  Conversion  is  combined  with  Transference.  Exam- 
ples of  the  latter  kind  are  in  a  kind  of  Epichirema,  as,  B  is 
A  ;  G  is  B,  for  it  is  non-D  ;  therefore,  C  is  A  ;  or  in  concrete 
matter  :  Vice  is  odious  ;  Avarice  is  a  vice,  for  it  is  unsympa- 
thizing  ;  therefore,  avarice  is  odious. 

In  the  same  way,  Mediate  Reasonings  are  combined  with 
one  another.  One  form  distinctly  treated  by  logicians,  and 
already  noticed,  is  the  Hypothetico-Disjunctive,  or  Dilemma. 
So  in  the  Sorites  manifold  combinations  of  the  several  proc- 
esses are  possible  within  the  limits  of  legitimate  Thought. 


METHODOLOGY  OF   REASONINGS.  187 

To  assure  certainty  in  all  such  instances  of  complicated 
reasoning,  the  rule  to  verify  each  distinguishable  process  by 
its  own  conditions,  is  the  one  simple  and  universally  efficient 
rule.  At  first,  as  in  arithmetical  computation,  the  procedure, 
being  thus  step  by  step,  will  necessarily  be  slow;  but  soon 
the  mind  acquires  power  to  analyze  and  verify  the  most  com- 
plicated processes  as  it  were  by  instinct,  precisely  as  after 
practice  it  reaches  by  one  leap  in  multiplication  the  product 
from  given  simple  factors,  without  going  through  the  many 
additions  involved,  or  attains  the  result  of  manifold  simpler 
processes  in  higher  applications  of  numerical  principles. 

§  114.  In  Logical  Conversion,  which  consists  in  the  simple 
transposition  of  the  terms  of  a  Judgment,  the  one 

,.  .  „  „  ,      .  .  .        Subjective 

condition  or  a  pertect  derivation  or  reasoning  is,   Law  of  con- 
that  the  quantity  of  the  terms  be  not  changed  in 
the  transposition. 

In  this  reasoning  the  Quality  of  the  Judgment  is  not  af- 
fected ;  the  derivation  respecting  simply  the  terms.  Now 
every  Judgment  being  essentially  an  identification  of  two 
objects  of  thought,  it  is  a  matter  of  indifference  to  Thought 
in  which  direction  the  movement  takes  place ;  whether  we 
say  A  =  B,  or  B  =  A.  If  we  may  say  the  one,  the  very 
nature  of  Thought  authorizes  us  to  say  the  other  also.  The 
problem  in  Conversion  is  this  :  Having  one  term  given  as 
subject  and  the  other  given  as  predicate,  how  with  the  main- 
tenance of  the  integrity  of  the  Thought  we  may  transpose 
these  terms.  We  could,  evidently,  do  this  as  freely  in 
Thought  generally  as  we  do  in  Algebraic  equations,  were  it 
not  that  for  the  most  part  the  language  of  Thought,  its  nota- 
tion, is  not  as  unequivocal  as  that  of  mathematical  science, 
The  Judgment  Alan  is  mortal  cannot  as  securely  be  con- 
verted as  we  convert  an  Algebraic  equation  by  transposing 
the  terms,  because  it  is  but  a  partial  Judgment,  whereas  all 
Algebraic  equations  are  properly  Identical  Judgments.  It 
means  only  that  one  of  the  characters  that  make  up  the 
notion  man,  is  identical  with  mortal ;  or  that  man  is  identical 


188  PURE  LOGIC. 

with  one  of  the  parts  that  make  up  the  class  mortal.  "When 
thus  interpreted,  the  conversion  becomes  as  simple  and  as 
certain  as  in  Algebra.  This,  then,  is  the  one  condition  of 
Simple  Conversion  :  that  no  more  and  no  less  be  expressed 
by  the  terms  after  the  transposition  than  was  thought  in  them 
before. 

Subjective  §  H*>.  In  Quantitative  Restriction,  the  one  con- 

Quantitative  <3itioti  of  perfect  Thought  is,  that  the  quantity 
Restriction,     thought  be  restricted  in  both  terms  in  equal  degree. 

The  only  difficulty  to  be  encountered  in  this  kind  of  reason- 
ing is  one  exactly  analogous  to  that  in  Conversion.  If  from 
the  Judgment  Man  is  rational  animal,  we  wish  to  derive  a 
Judgment  restricted  in  the  subject  only,  as,  this  man,  Ameri- 
can men,  &c,  are  rational  animal,  we  do  it  without  fear  of 
fallacy,  because  we  interpret  the  datum  at  once  in  Extensive 
Quantity,  and  derive  the  restricted  Judgment  as  meaning  that 
a  part  of  the  subject  man  is  part  of  the  class  rational  animal. 
But  we  should  with  equal  legitimacy  be  able  to  restrict  the 
predicate  also.  We  can  do  this,  however,  under  our  ordinary 
use  of  language,  only  as  we  rather  force  the  interpretation  by 
viewing  the  proposition  in  its  Comprehensive  Quantity  ;  then 
the  difficulty  vanishes.  Thus,  if  we  explicate  it,  the  notion 
man  contains  in  it,  as  one  of  its  component  characters,  that 
of  rational,  this  being  one  of  the  complement  of  attributes 
rational  animal ;  we  recognize  the  validity  of  the  process. 
We  then  reason :  The  notion  man  contains  the  composite 
attribute  rational  animal;  therefore,  it  contains  the  attri- 
bute rational.  In  like  manner:  Man  is  rational;  therefore, 
he  is  intelligent. 

It  will  be  observed  that  if  another  judgment  be  required 
in  order  to  show  that  the  new  predicate  is  a  part  of  the  pred- 
icate in  the  sumption,  the  mediate  reasoning  or  the  syllogism 
will  be  called  forth. 

§  116.  In  Modal  Restriction,  the  one  condition  of  perfect 
Subjective  thought  is,  that  the  restriction  follow  the  order  of 
Modal  logical  descent  from  the  Apodictic  to  the  Assertory 

Restriction.     an(j  Problematic  ;  from  the  Assertory  to  the  Prob- 


METHODOLOGY  OF  REASONINGS.  189 

lematic.  If  the  modal  restriction  be  carried  further  into 
lower  degrees  of  the  Contingent,  as  may  be  done  by  means 
of  the  adverbs  of  modality,  then  the  law  requires  that  the  re- 
striction be  from  the  higher  to  the  lower,  and  never  the  re- 
verse. Thus  from  necessarily  true  we  may  infer  to  the 
actually  true,  or  to  the  probably  true  or  possibly  true,  not  con- 
versely. 

§  117.  In  Immediate  Reasonings  by  Transference,  there 
are  two  distinct  kinds  —  one  consisting  in  the  transference 
of  Quality,  the  other  in  the  transference  of  Modality  from 
the  copula  of  the  Judgment  to  the  terms.  It  was  shown  in 
the  former  Part,  §  63,  that  in  order  to  preserve  the  integrity 
and  purity  of  the  Thought,  it  is  necessary  to  keep  the  trans- 
ference within  the  strict  lines  of  Thought ;  that  is,  since 
Thought  can  recognize  only  the  relations  of  Whole  and 
Part  in  its  object-matter,  all  legitimate  transference  must  be 
within  the  limits  of  those  relations.  In  Transference  of 
Quality,  accordingly,  the  condition  of  perfect  thought  is,  that 
the  terms  must  be  recognized  as  under  the  same  Whole. 
Thus,  in  the  proposition  A  is  not  B,  in  order  to  transfer  the 
negation  from  the  copula  to  the  predicate,  so  as  to  infer  A  is 
non-B,  A  and  B  must  be  recognized  as  being  in  the  same 
Whole.  From  the  proposition  :  The  scorpion  is  not  verte- 
brate, we  may  legitimately  infer  the  proposition,  The  scor- 
pion is  invertebrate,  only  as  we  can  recognize  the  term  scor- 
pion as  belonging  to  the  Whole  animal  of  which  vertebrate 
and  invertebrate  are  complementary  parts. 

In  the  other  kind  of  Transference,  that  by  transfer  of 
Modality,  as,  A  is  possibly  B,  therefore,  A  is  a  possible  B, 
there  is  need  of  the  same  caution  not  to  slip  a  quality  of 
the  thought  surreptitiously  over  to  the  matter.  If  in  the  de- 
rived proposition,  possible  be  interpreted  as  pertaining  still  to 
the  copula,  as  it  may  be,  there  is,  of  course,  no  proper  logical, 
but  only  a  verbal,  transference.  But  if  it  be  taken  as  limit- 
ing the  term  B,  then  it  can  be  a  legitimate  process  of  thought 
only,  as  in  the  case  of  Transference  of  Quality,  when  the 


190  PURE  LOGIC. 

term  as  before  transfer  and  the  term  as  after  transfer  are  com- 
plementary parts  of  a  whole  of  which  the  other  term  must 
be  a  lower  part.  Thus  we  cannot  from  the  proposition 
Sponge  may  be  animal,  that  is,  Sponge  is  possibly  animal, 
infer  Sponge  is  possible  animal,  that  is,  has  all  the  charac- 
ters which  make  up  the  concept  animal,  and  only  lacks  the 
character  real.  But  from  the  proposition  Sponge  may  be  an 
animal,  we  may  infer  Sponge  is  a  possible  animal,  having 
recognized  it  as  possessing  the  essential  character  of  an  ani- 
mal—  to  wit :  an  alimentary  cavity. 

§  118.  Of  derivations  of  Judgments  by  Disjunction  and 
by    Composition,    it    is   unnecessary    to    add   to 

Disjunction         "  . 

and  compo-  what  has  been,  in  the  First  Part,  §§  64,  65,  indi- 
cated as  constituting  the  essential  conditions  of  the 
two  processes. 

§  119.  In  the  Categorical  Deductive  Syllogism,  the  sub- 
jective conditions  of  perfect  thought  are : 

1°.  That  there  be  three  and  only  three  terms  bearing  the 
relation  to  each  other  of  Major,  Middle,  and  Minor ;  the 
Middle  being  contained  in  or  under  the  Major,  and  containing 
the  Minor. 

2°.  That  the  Sumption  affirm  or  deny  the  Major  to  con- 
tain the  Middle  term,  and  the  Subsumption  affirm  the  Middle 
to  contain  the  Minor  term. 

3°,  That  the  Conclusion  affirm  or  deny  the  Major  to  con- 
tain the  Minor  term,  according  as  the  Sumption  affirms  or 
denies. 

4°.  That  the  Thought  in  the  Conclusion  be  not  illegiti- 
mately changed  to  a  higher  modality  than  in  the  Antecedent. 

The  first  part  of  this  Law  requires  that  the  Middle  Term 
be  recognized  as  standing  in  the  relation  of  containing  Whole, 
and  contained  part  in  the  same  kind  of  Whole,  to  the  Major 
and  Minor  terms  respectively.  Violations  of  this  Law  in- 
volve the  following  fallacies  :  — 

The  fallacy  of  using  the  word  expressing  the  middle  term 
in  two  different  senses  in  the  two  premises.     This  fallacy  ia 


METHODOLOGY  OF  REASONINGS.  191 

called  the  Logical  Quadruped,  as  it  really  introduces  four 
terms  instead  of  three  into  the  Reasoning,  and  thus  makes  it 
go,  as  it  were,  on  four  feet.  If  the  term  is  expressed  by  a 
single  word,  the  fallacy  is  called  simply  an  Equivocation  ;  if 
in  a  phrase,  it  is  called  an  Amphibology.  The  following  are 
examples :  Mies  est  syllaba  ;  mus  caseum  rodit ;  ergo,  syllaba 
caseum  rodit. 

Herod  is  a  fox  ;  a  fox  is  a  quadruped  ;  therefore,  Herod  is 
a  quadruped. 

Air  is  ponderable  ;  spirit  is  air  ;  therefore,  spirit  is  pon- 
derable. 

You  should  eat  what  is  sold  in  the  market ;  raw  meat  is 
sold  in  the  market ;  therefore,  you  shoidd  eat  raw  meat. 

Seven  and  two  are  odd  and  even  numbers  ;  nine  is  seven 
and  two  ;  therefore,  nine  is  odd  and  even.  This  last  is  an 
example  of  what  is  called  the  Fallacy  of  Composition  and 
Division,  in  which  the  middle  term  is  used  in  one  premise 
in  its  composite  sense,  in  the  other,  in  its  distributive. 

The  king  can  do  no  wrong  ;  Herod  was  king  ;  therefore,  he 
was  innocent.  This  is  an  example  of  the  Fallacy  a  dicto  se- 
cundum quid  ad  dictum  simpliciter,  consisting  in  the  use  of  a 
word  employed  in  one  relation  in  one  premise,  and  in  another 
relation  or  without  relation  in  the  other. 

To  this  class  belongs  also  the  Fallacy  of  Unreal  Univer- 
sality, as,  The  Cretans  are  liars ;  Epimenides  is  a  Cretan  ; 
therefore,  Epimenides  is  a  liar.  The  word  expressing  the 
middle  term  in  the  Subsumption  denotes  the  whole  class  of 
Cretans  ;  in  the  Sumption,  it  denotes  only  a  large  part  of  the 
class. 

In  these  fallacies  there  is  a  term  which  stands  in  each 
of  the  premises  expressed  by  the  same  word ;  but  as  this 
word  is  used  in  two  different  meanings,  we  have  really  two 
terms  ;  consequently  there  is  no  mediation  of  the  Judgment 
—  no  proper  derivation,  no  true  reasoning. 

The  fallacy  in  probation  called  peiitio  principii,  Begging 
the  Question,  also,  is  to  be  detected  by  this  Law.     It  con- 


192  PURE  LOGIC. 

sists  in  taking  as  one  of  the  premises  a  proposition  equally- 
needing  proof  as  the  conclusion  itself.  It  appears  in  divers 
forms.  First,  generally,  when  a  premise  is  assumed  which 
is  as  much  denied  by  the  party  addressed  as  the  proposition 
to  be  proved ;  as,  when  it  is  attempted  to  prove  the  Divinity 
of  Christ  to  a  Mohammedan  from  the  authority  of  the  Bible 
which  he  rejects  ;  or  the  cause  of  the  planetary  motion  to  be 
an  ethereal  vortex.  This  is  the  petitio  principii  proper;  but 
the  name  has  been  applied  to  fallacies  generally  which  lie  in 
an  illicit  premise. 

A  second  form  of  this  fallacy,  the  petitio  principii,  is  the 
Hysteron  proteron,  in  which  the  truth  of  the  antecedent  is 
dependent  upon  the  conclusion ;  as,  when  Scriptural  testi- 
mony is  urged  in  favor  of  the  Being  of  God  ;  Scriptural 
testimony  being  valid  only  as  it  is  the  testimony  of  God,  and 
therefore  presupposing  his  existence. 

A  third  form  of  the  petitio  principii,  is  the  Circle,  in 
which  the  conclusion  is  disguised  in  one  of  the  premises  ;  as, 
Lead  falls  to  the  ground  quicker  than  feathers,  because  it  is 
heavier. 

This  vice  is  just  the  reverse  of  that  in  the  Logical  Quad- 
ruped ;  as  here  the  same  meaning  is  conveyed  in  different 
language,  so  that  there  appear  to  be  two  distinct  proposi- 
tions, while  really  there  is  but  one.  In  the  Logical  Quadru- 
ped, on  the  other  hand,  two  different  meanings  are  hidden 
under  the  same  guise  of  words.  Dr.  Whately  has  well  ob- 
served that  the  English  language  peculiarly  favors  this  fal- 
lacy, as  we  may  express  the  same  thought  in  Saxon  or  in 
Norman  words  ;  thus  :  "  To  allow  every  man  unbounded  free- 
dom of  speech  must  be  best  for  the  State ;  for  it  is  highly 
conducive  to  the  interests  of  the  community  that  each  indi- 
vidual should  possess  unlimited  liberty  of  expressing  his 
sentiments." 

Still  another  fallacy  in  probation  is  the  Saltus,  in  which 
one  of  the  premises  is  neither  expressed  nor  necessarily  im- 
plied.    This  fallacy  is  practicable  only  by  reason  of  the  cir- 


METHODOLOGY  OF  REASONINGS.  193 

curastnnce  that  the  Enthymeme  is  ordinarily  admitted  in 
place  of  the  full  reasoning.  To  verify  an  Enthymeme,  it 
becomes  necessary  to  supply  the  suppressed  premise,  when 
this  vice  in  the  thought  at  once  shows  itself. 

Further,  it  is  implied  in  the  rule  that  the  terms  be  signif- 
icant, —  contain  veritable  thought.  If,  therefore,  in  the  course 
of  the  reasoning,  a  term  become  insignificant,  be  a  zero  in 
thought,  the  reasoning  is  fallacious.  This  is  exemplified  in 
the  familiar  Algebraic  demonstration  that  7  =  23.  For  put- 
ting x=7  and  y  =  23,  then  as  x  -\-  y  =  x  -f-  y,  and  so  ax  -(- 
ay  =  ax  -\-  ay,  and  by  transposition  ax  —  ax^=.ay  —  ay,  we 
have,  by  dividing  by  a  —  a,  x=:y  or  7  =  23. 

Fallacies  under  the  second  part  of  the  Law  are  liable  to 
occur  when  it  is  not  clearly  distinguished  which  is  the  sump- 
tion and  which  the  subsumption,  so  that  the  middle  and  minor 
terms  are  really  differenced,  instead  of  the  major  and  middle  ; 
in  other  words,  the  subsumption  is  of  negative  quality.  Thus, 
Men  are  mortal ;  angels  are  not  men  ;  therefore,  angels  are 
not  mortal;  or,  Men  are  mortal;  brutes  are  not  men  ;  there- 
fore, brutes  are  not  mortal. 

Fallacies  under  the  third  part  of  the  Law  are  such  as  fol- 
lows :  Wise  and  good  men  were  condemned  by  the  Athenian 
populace  ;  Socrates  was  condemned  by  the  Athenian  populace  ; 
therefore,  he  was  a  wise  and  good  man.  Here  the  conclu- 
sion has  for  its  terms  the  minor  and  the  middle.  There  is 
really  no  subsumption  in  this  example,  as  the  middle  and  the 
minor  terms  are  compared  only  in  the  conclusion. 

Here  belongs  also  the  famous  Fallacy,  called  Ignava  Ratio, 
or  Lazy  Reason ;  also  the  Reaper,  the  Controlling  Reason, 
the  Argumentum  de  Fato.  Cicero  thus  states  it :  If  it  be 
fated  that  you  recover  from  your  present  disease,  whether  you 
call  in  a  doctor  or  not,  you  will  recover ;  again,  If  it  be  fated 
that  you  do  not  recover  from  your  present  disease,  whether  you 
call  in  a  doctor  or  not,  you  will  not  recover :  but  one  or  other 
of  the  contradictories  is  fated ;  therefore,  to  call  in  a  doctor 
is  of  no  consequence. 
13 


194  PURE  LOGIC. 

Although  it  appears  here  in  the  form  of  a  Hypothetico- 
Disjunctive  Syllogism,  and  thus  appears  more  plausible  and 
difficult  to  detect,  it  is  easily  reducible  to  a  Categorical  De- 
ductive, thus  :  What  is  fated  is  unavoidable  by  any  exertion  ; 
the  alternative  of  recovery  from  this  sickness  or  death  is  fated  ; 
therefore,  the  issue  alike  whether  recovery  or  death  is  unavoid- 
able by  any  exertion.  The  sophism  thus  reduced  is  a  pal- 
pable amphibology ;  the  conclusion  has  not  the  same  term  as 
minor  that  is  contained  in  the  subsumption ;  —  in  the  latter 
proposition  it  is  an  alternative  of  which  something  is  predi- 
cated, while  in  the  conclusion  it  is  of  the  two  factors  of 
the  alternative  taken  separately  of  which  the  predication  is 
made.  The  only  valid  conclusion  is  :  The  alternative  of  re- 
covery or  death  is  unavoidable  by  any  exertion ;  which  is  a 
very  different  proposition  from  this  :  This  alternative,  whether 
the  one  or  the  other — whether  recovery  or  death  —  occur,  is 
beyond  the  power  of  exertion  to  determine. 

By  the  application  of  this  part  of  the  Law,  further,  we 
may  expose  most  of  the  diverse  fallacies  in  probation  classed 
under  the  generic  name  of  mutatio  elenchiy  in  the  sense  of 
change  of  the  issue.  The  conclusion  being  the  proposition 
which  was  originally  in  doubt  and  was  to  be  proved,  if  the 
terms  are  not  the  same  as  in  the  original  doubt  a  fallacy 
arises.  Thus,  if  a  person  should  undertake  to  prove  the 
existence  of  ghosts,  and  should  only  prove  some  unusual 
noises  and  appearances  during  the  night,  he  would  exemplify 
this  kind  of  fallacy. 

The  violation  of  the  fourth  part  of  the  Law  may  occur  in 
two  different  forms,  the  first  when  a  necessary  Judgment 
is  derived  from  an  assertory  or  problematic,  or  an  assertory 
from  a  problematic  ;  and  the  second,  when  the  modality  of 
the  thought  is  covertly  transferred  to  the  matter. 

The  first  form  may  be  exemplified  thus :  It  rains  when 
the  moon  changes  ;  the  moon  changes  to-morrow  ;  therefore,  it 
must  rain  to  morrow. 

Of  the  second  the  following  is  an  example :  For  aught  we 


METHODOLOGY  OF  REASONINGS.  195 

know  the  deaf  may  be  sensible  of  sounds  within  the  ordinary 
hearing  distance ;  the  deaf  mute,  Laura  Bridgman,  was 
within  that  distance  when  her  teacher  spoke  to  her  ;  therefore, 
Laura  coidd  have  heard  the  direction  of  her  teacher. 

The  common  Fallacy  of  Non  causa  pro  causa,  or  Post  hoc, 
ergo  propter  hoc,  in  which  only  general  antecedence  is  ac- 
cepted as  universal,  or  a  causal  connection  is  inferred  from 
such  general  antecedence,  belongs  under  this  species.  This 
variety  of  fallacy  is  extremely  common ;  but  like  popular 
reasonings  it  is  generally  in  the  form  of  an  Enthymeme,  the 
sumption  being  suppressed.  Thus :  The  moon  will  change 
to-morrow  ;  therefore,  it  must  rain  to-morrow. 

§  120.  In  the  Categorical  Inductive  Syllogism,  the  sub- 
jective conditions  of  perfect  thought  are : 

1°.  That  there  be  three  and  only  three  terms,  two  of 
which  bear  the  relation  to  each  other  of  Part  and  Comple- 
mentary Part,  and  the  third  bears  the  relation  of  Whole 
alike  to  each  of  these  two. 

2°.  That  the  Sumption  affirm  or  deny  this  third  of  one  of 
the  other  two,  and  the  Subsumption  affirm  these  two  to  be 
Complementary  of  each  other. 

3°.  That  the  Conclusion  affirm  or  deny  the  third  of  that 
term  of  which  it  is  not  predicated  in  the  Sumption. 

4°.  That  the  Modality  be  not  illegitimately  changed. 

Of  the  application  of  this  general  Law  of  the  Inductive 
Syllogism,  it  will  be  unnecessary  to  speak  in  detail,  except 
in  respect  to  the  one  feature  in  which  it  differs  from  the  De- 
ductive. This  peculiar  element  in  the  Law  is  in  the  second 
part  which  requires  that  the  Subsumption  affirm  two  of  the 
terms  to  be  complementary  of  each  other,  and  the  main  dif- 
ficulty is  in  the  objective  bearings  of  the  rule,  in  verifying 
this  premise  as  a  true  judgment.  As  in  Deductive  Reason- 
ing, so  in  Inductive  and  to  a  much  greater  extent,  a  part  of 
the  Antecedent  is  usually  suppressed  in  discourse ;  and  inas- 
much as  logical  literature  has  confined  itself  mainly  to  the 
former,  we  are  less  familiarized  with  the  process  of  supplying 


19(3  PURE  LOGIC. 

the  suppressed  part  in  Induction  in  order  to  verify  the  rea- 
soning. There  is  still  another  difficulty  arising  from  the 
fact  that  this  reasoning  more  commonly  proceeds  in  Causal 
Wholes  with  which  logical  systems  have  concerned  them- 
selves as  little  as  with  Induction,  and  with  the  movements 
of  Thought  generally  in  the  relation  of  Part  and  Comple- 
mentary Part. 

As  Logical  Methodology  aims  to  guide  to  true  Science  by 
unfolding  the  conditions  of  perfect  thought,  both  material 
and  formal,  and  as  all  proper  thought  is  under  the  general 
relationship  of  Whole  and  Part,  including,  of  course,  that  .of 
Part  and  Complementary  Part,  we  shall  more  intelligently 
and  securely  reach  the  conditions  of  a  true  Induction  by 
illustrating  the  process  in  its  application  to  the  several  kinds 
of  quantity  separately. 

And,  first,  in  proper  logical  wholes  —  the  wholes  of  Ex- 
tension and  Comprehension.  These  wholes,  we  have  seen, 
are  the  pure  products  of  thought.  We  have  seen  how  they 
are  produced ;  how  concepts  are  formed  by  a  synthesis  of 
the  homologous  terms  of  two  or  more  judgments  having  the 
same  analogous  term,  which  we  have  called  the  Base  of  the 
concept.  We  have  seen  how  concepts,  thus  springing  into 
existence  in  the  progress  of  human  intelligence,  at  once  em- 
body themselves  in  words.  We  have  seen  how  by  two 
movements  in  opposite  directions  but  perhaps  synchronous, 
according  as  the  subject  or  the  predicate  of  the  primitive 
judgments  is  taken  as  the  Base,  the  concept  and  its  embodi- 
ment —  the  word  becomes  narrowed  or  extended,  whether  by 
occasion  of  the  more  extended  observation  cf  its  matter,  and 
the  consequent  rectification  of  its  objective  import,  or  of  the 
needs  of  thought  for  fuller  or  more  discriminating  symbols. 
Now  these  concepts  so  formed  and  modified,  and  these  words, 
their  verbal  embodiments,  may  become  matter  of  thought — ■ 
matter  of  inductive  thought.  They  are  accepted  as  its  data. 
If  they  have  been  perfectly  formed,  then  the  inductive 
process  begins  with  objective  truth.     So  in  fact  it  ordinarily 


METHODOLOGY  OF  REASONINGS.  197 

begins.  It  is  obvious  that  just  so  much  of  contingency  as 
attaches  to  the  original  data  as  thus  furnished  by  the  con- 
spiring and  restless  energies  of  all  who  use  the  language  and 
formed  the  concept,  must  attach  to  the  results  of  the  induc- 
tion itself ;  and,  so  far  as  its  material  perfection  is  concerned, 
no  more. 

We  will  now  look  at  the  subjective  element  —  the  induc- 
tive process  itself —  to  see  how  far  necessary  certainty  may 
attach  to  it,  and  how  far  this  process  may  be  relied  on  to  ad- 
vance knowledge.  It  is  apparent  at  once,  from  the  very 
nature  of  a  concept,  then,  that  the  Base  of  the  concept,  and 
any  part  of  the  Base,  must  belong  to  every  part  of  the 
concept  itself  alike.  If  horse,  ox,  dog,  are  parts  of  the  con- 
cept quadruped,  then  the  Base  on  which  the  concept  was 
formed,  four-fooled,  and  every  part  of  four-footed,  must  be- 
long to  each  part  alike,  to  horse,  ox,  dog.  Now  in  Induction 
as  applied  to  concept  wholes,  the  problem  is  simply  this : 
Given  horse  as  four-footed  for  one  premise,  and  given,  also, 
ox,  dog,  as  complementary  part  of  horse,  as  the  other  part  of 
the  antecedent,  and  we  induce  with  absolute  certainty  that 
ox,  dog,  are  four-footed.  This  is  but  retracing  the  steps  by 
which  the  concept  was  formed  —  the  analysis  of  the  original 
synthesis  ;  and  if  that  was  true,  the  result  of  the  induction 
is  also  true. 

"While  unhesitating  assent  must  be  yielded  to  this  repre- 
sentation of  the  validity  of  the  inductive  process,  yet  it  may 
remain  in  doubt  whether  there  be  any  advance  made  in  any 
real  knowledge,  as  we  seem  to  have  no  more  than  we  had 
when  we  formed  the  concept.  But  a  brief  reflection  will 
convince  us  that  induction  in  mere  concepts  —  the  pure  prod- 
ucts of  human  thought,  —  gives  to  each  of  us  a  large  share 
of  all  the  knowledge  we  severally  possess.  Concepts,  words, 
are  not  the  product  of  one  individual  thought,  but,  so  to 
speak,  of  the  conspiring  thought  of  the  race.  Each  thinker 
has  contributed  to  their  formation  and  modification.  How 
much,  for  instance,  quadruped  imports,  has  been  determined 


198  PURE  LOGIC. 

by  this  conspiring  thought.  If  all  that  forming,  shaping 
thought  could  be  imagined  to  he  garnered  up  in  one  body  of 
living  activity,  preserving  the  entire  complicated  movement 
that  shaped  the  concept,  then  to  such  an  activity  no  advance 
of  knowledge  could,  perhaps,  be  supposed  to  be  effected  by 
the  analysis  of  the  forming  movement  in  induction.  But 
the  fact  is  that  no  individual  thinker  contributes  more  than 
the  minutest  fraction  to  the  whole  formation.  To  the  indi- 
vidual, therefore,  the  analysis  may  bring  all  the  knowledge 
that  was  possessed  by  all  the  contributors  to  the  formation. 
But,  farther,  the  work  of  forming  concepts  and  concept- 
words  is  a  silent,  unintentional,  and  so  far  unconscious  work, 
even  on  the  part  of  their  very  framers.  They  are  the  spon- 
taneous, instinctive  product  of  man  as  a  social  organism,  as 
a  thinking  and  speaking  yet  cooperative  nature.  The  very 
creator  of  language  can  know  his  own  product  only  as  he 
can  take  to.  pieces  again  the  wondrous  complication.  Induc- 
tion, thus,  is  the  condition  and  chief  means  not  only  of  indi- 
vidual progress  in  intelligence,  but  of  that  of  the  community, 
the  race.  Accordingly,  a  great  part  of  the  advance  of 
knowledge  on  the  part  of  individual  learners  consists  in  the 
resolution  of  concepts  by  a  proper  induction  —  by  inducing 
the  Base  or  parts  of  the  Base  from  any  given  part  to  any 
proper  complementary  part. 

Not  only  this,  but  the  sum  of  human  knowledge  is  aug- 
mented more  by  Induction  than  by  any  other  of  the  proceshes 
of  thought,  if  it  be  possible  to  separate  in  such  a  comparison 
mutually  dependent  processes.  This  will  appear  at  once 
from  the  consideration  that  while  the  enlargement  of  the 
Base  of  the  concept  may  be  effected  by  observation  applied 
to  any  one  part  of  it,  every  such  enlargement  enures  to  the 
spread  of  our  knowledge  over  all  the  parts.  Thus,  in  the 
concept  quadruped,  if  an  observer  of  nature  discover  in  his 
inspection  of  an  individual  horse  a  pi'eviously  unknown  prop- 
erty or  character  belonging  to  it  so  far  as  quadruped,  we 
will  suppose  some  structure  of  a  joint  necessary  to  the  mo- 


METHODOLOGY  OF  REASONINGS.  199 

tion  of  such  an  animal,  before  unnoticed,  he  not  only  induces 
from  the  individual  horse  observed  to  every  other  horse,  but 
to  every  other  quadruped.  Nor  does  the  increase  of  knowl- 
edge originating  in  this  single  discovery  stop  here.  But 
from  this  property  other  properties  may  be  induced  indefi- 
nitely, as  to  mode  of  locomotion,  position,  and  numberless 
other  relations  of  other  parts  of  the  animal  structure,  habits 
of  life  even,  and  utilities  without  end. 

Subjectively,  then,  Induction  in  concepts  bears  the  charac- 
ter of  absolute  certainty.  Objectively,  it  bears  the  charac- 
ter of  contingency  which  attaches  to  the  datum  —  the  con- 
cept itself.  This,  however,  as  the  legitimate  product  of 
mankind  as  speech-forming,  is  to  be  accepted  as  valid. 
Here  more  than  anywhere  else  does  the  adage  hold  true  — 
Vox  populi,  vox  Dei  ;  —  the  conspiring  thought  of  the  race 
is  the  thought  of  truth.  Even  the  skeptic  accepts  the  con- 
cept as  valid ;  he  could  not  advance  a  step  in  his  argumenta- 
tion but  as  he  is  supported  on  the  truth  of  concepts.  More- 
over, Induction  is  not  only  a  valid  instrument  of  knowledge, 
it  is  a  chief  instrument  of  knowledge  to  thinking,  speaking 
man.  And  the  simple  condition  of  perfect  thought  which 
shall  give  us  assured  truth  or  perfect  science  is  that  we 
keep  within  the  relationship  of  part  to  complementary  part. 
This,  however,  is  by  no  means  difficult  in  case  of  concept 
wholes.  The  chief  liability  to  fallacious  reasoning  lies  in 
our  not  rightly  apprehending  the  base  of  the  concept. 

Induction  in  the  wholes  proper  to  the  object-matter  of 
thought,  bears  the  same  character  of  subjective  certainty. 
That  the  part  necessitates  its  complementary  part  is  a  neces- 
sary truth. 

Objectively,  the  validity  of  Induction  in  this  kind  of  wholes 
depends  on  the  truth  of  the  data,  first,  that  the  given  part  is 
a  part  of  the  whole  object  thought ;  secondly,  that  the  other 
part  is  truly  complementary.  In  an  Integrate  Whole,  thus, 
if  head  be  given  as  part  of  man,  and  body  be  given  as  com- 
plementary part,  then  we  may  induce  that  whatever  is  true  of 


200  PURE  LOGIC. 

head  as  part  of  man  —  for  instance,  organic  —  is  true  of  body  ; 
while  we  induce  the  different  of  it  as  complementary  ;  thus, 
if  head  is  higher,  body  is  lower ;  if  head  is  guiding,  body  is 
guided,  and  the  like. 

In  a  Substantial  Whole,  if  bi-manous  be  given  as  part  of 
man  as  physical,  and  mammal  as  complementary,  then  what- 
ever of  physically  human  may  be  true  of  bi-manous  as  part, 
cellular,  for  instance,  may  be  induced  of  mammal ;  while,  on 
the  other  hand,  we  may  induce  of  it  as  complementary,  the 
different ;  as  that,  if  bi-manous  is  prehensile,  mammal  is 
non-prehensile.  In  the  same  way  if  rational  spirit  be  given 
to  us  as  a  substance  having  the  attributes  of  intelligent,  emo- 
tional, and  voluntary,  we  may  induce  that  whatever  is  true 
of  intelligent  simply  as  part  of  rational  spirit  is  true  of  emo- 
tional and  voluntary,  as,  for  instance,  that  they  are  active, 
capable  of  growth,  dependent  on  conditions,  limited,  and  the 
like  ;  and  also  as  complementary,  that  they  are  not  cognitive, 
not  reasoning,  and  the  like. 

So  in  a  Causal  Whole,  if  the  cause  with  one  part  of  its 
effect  be  given,  we  may  induce  to  the  complementary  effect 
the  same  and  also  the  different.  If,  thus,  solar  heat  be  given 
as  cause,  and  this  piece  of  expanded  iron  be  given  as  part 
effect,  we  may  induce  the  same  of  every  piece  of  iron  within 
the  sphere  of  the  causal  agency.  So  if  there  be  given  a 
causal  agency  in  creating,  which  produces  a  flower  with  a 
definite  number,  order,  figure,  color  of  organs,  and  a  definite 
fragrance,  we  induce  the  same  of  every  other  flower  within 
the  same  causal  sphere.  The  principle  of  Induction,  that 
the  part  necessitates  its  complementary  part,  holds  here  as 
everywhere  else.  The  peculiar  difficulty  here  lies  in  ob- 
serving the  objective  law  of  induction  —  in  verifying  the 
data,  determining  the  causal  whole  and  the  complementary 
parts.  All  the  numerous  rules  prescribed  in  material  Induc- 
tion so  called,  are  comprehended  in  this  one  objective  law  of 
Induction  —  Verify  the  parts  as  complementary  of  each  other 
in  the  same  causal  whole.     This  principle  will  determine 


METHODOLOGY   OF  REASONINGS.  201 

whether  one  observation  or  more  are  necessary.  One  obser- 
vation may  in  some  cases  be  sufficient  to  ascertain  the  exist- 
ence of  the  cause,  its  sphere,  its  liability  to  be  overborne  by 
other  causal  agencies,  or  to  be  hindered  by  failing  conditions, 

may,  in  short,  verify  the  data.     In  other  cases  more  may 

be  required  ;  and  how  many  may  be  requisite  must  be  deter- 
mined by  the  occasions  of  the  induction  or  by  the  specific 
peculiarities  of  its  object-matter. 

All  this  is,  however,  aside  from  the  proper  design  of  pure 
logic.     It  belongs  to  Applied  Logic  to  prescribe  the  mode  of 
ascertaining    the  causal   sphere,    to   indicate    the  degree  of 
contingency  that  attaches  to  the  matter,  the  datum  attained 
for  the  inductive  process,  and  by  what  methods,  if  by  any, 
that  degree  may  be  reduced  to  a  minimum.     It  is  impossible 
to  eliminate  all   contingency  ;  for,  as  has  been  shown,  the 
necessary  lies  exclusively  in  the  realms  of  thought,  and  all 
that  is  foreign  to  thought  must  bear  the  character  of  contin- 
gent.    But  this  contingency  may  be,  for  any  particular  use 
in  our  thinking,  an  infinitesimal ;  and  thought   may  accept 
the  datum  as  not  to  be  questioned.      In  fact,  we  do  accept 
the  reality  of  External  Existence  ;  we  accept  the  reality  of 
Being,  both  as  Substance  having  attributes,  and  as  Cause  pro- 
ducing effects ;  we  accept  the  diversity  and  the  stability  of 
things  —  that  each  thing,  whether  substance  or  cause,  has  its 
own  permanent  attributes,  so  that  each  substance  will  retain 
each  essential  property  that  it  is  now  found  to  possess,  for  to- 
morrow and  the  next  year,  and  each  cause  work  its  own  proper 
effect  here  and  elsewhere  alike.     The  contingency  that  rises 
in  all  this  we  dismiss  from  our  thought,  and  treat  such  matter 
as  true  beyond  impeachment.     But  when  we  pass  one  step 
further,  and  endeavor  to  ascertain  the  real  diversity  of  sub- 
stances with  their  several  properties  and  of  causes  with  their 
several  effects,  we  come  upon  a  contingency  that  may  inval- 
idate our  whole  thought-process  applied  to  it.     We  cannot 
induce  that  any  one  property  which  belongs  to  a  given  sub- 
stance to-day  will  be  found  to  belong  to  it  to-morrow,  or  be- 


202  PURE  LOGIC. 

longs  to  a  substance  having  all  the  other  properties  elsewhere, 
until  we  have  discriminated  it  as  an  essential  property,  not 
an  accidental  one ;  we  cannot  induce  that  any  one  effect 
which  we  find  to-day  proceeding  from  a  given  cause  before 
us  will  be  found  proceeding  from  it  to-morrow,  or  from  a 
cause  working  all  the  other  effects,  but  working  elsewhere. 
How  to  discriminate  the  essential  from  the  accidental,  it  is 
the  province  of  Applied  Logic  in  each  department  of  knowl- 
edge to  indicate  —  to  determine  by  what  methods,  and  to  what 
extent  these  methods  must  be  carried  that  the  contingency 
may  be  reduced  to  the  requisite  degree,  and  to  prescribe  the 
tests,  and  checks  also,  as  well  as  the  methods  of  observation. 
Such  a  science,  both  in  its  general  principles  and  also  in  its 
bearing  on  each  of  the  departments  of  knowledge,  is  a  great 
desideratum,  as  well  for  the  more  rapid  advancement  of  science 
as  for  its  verification.  Not  a  little  will  be  gained,  however, 
in  the  interest  of  human  knowledge,  if  the  thought-process 
be  carefully  discriminated  from  the  matter  to  which  it  is  ap- 
plied, and  its  nature  and  laws  be  well  understood.  And  a 
further  gain,  by  no  means  inconsiderable,  will  also  be  secured, 
if  it  is  ascertained  precisely  what  is  to  be  done  in  construct- 
ing a  methodology  for  any  particular  field  of  scientific  induc- 
tion, in  so  far  as  regards  the  several  conditions  of  perfect 
science. 

§  121.  In  the  Hypothetical  Syllogism,  the  Law  of  perfect 
cognition  requires  — 

1°.  That  the  premises,  the  terms  of  which  are  here  Judg- 
ments, be  recognized  and  verified,  and  particularly  the  mode 
of  relation  which  is  affirmed  between  the  terms  of  the  Sump- 
tion, whether  that  of  Whole  to  Part,  or  of  Part  to  Comple- 
mentary Part. 

2°.  That  the  Conclusion  affirm  the  consequent  member  of 
the  Sumption  in  the  Affirmative  or  Ponent  form,  and  deny 
the  antecedent  member  in  the  Negative  or  Tollent  form  of 
the  Syllogism. 

The  difficulty' in  respect  to  the  first  or  objective  condition 


METHODOLOGY  OF  REASONINGS.  203 

of  a  valid  Hypothetical  Reasoning  is  twofold  :  that  of  sup- 
plying the  part  of  the  antecedent  which  is  suppressed ;  and 
that  of  distinguishing,  in  order  to  verification,  the  character 
of  the  Sumption,  whether  it  expresses  the  relation  of  Whole 
to  Part,  or  of  Part  to  Complementary  Part.  Either  premise 
may  be  suppressed,  and  in  either  relation  of  the  terms  of  the 
Sumption.  Thus  we  may  reason,  either:  If  the  sun  had 
arisen,  it  must  have  been  light;  therefore,  the  sun  could  not 
have  arisen,  suppressing  the  subsumption  ;  or,  The  sun  had 
arisen ;  therefore,  it  was  light,  suppressing  the  sumption. 
We  may  also  reason :  If  virtue  is  voluntary,  vice  is  volun- 
tary;  therefore,  vice  is  voluntary,  suppressing  the  subsump- 
tion, but  virtue  is  voluntary  ;  or,  Virtue  is  voluntary ;  there- 
fore, vice  is  voluntary,  suppressing  the  sumption. 

One  of  the  chief  liabilities  to  error  in  the  subjective  ele- 
ment of  the  reasoning  arises  in  the  negative  form,  when  the 
antecedent  member  of  the  sumption  is  also  negative,  from 
the  doubling  of  negatives  ;  as,  If  vice  be  not  voluntary,  virtue 
must  be  necessitated;  but  virtue  is  not  necessitated;  there- 
fore, vice  is  not  voluntary.  Here  the  fallacy  is  obvious  ;  but 
it  may  be  covered  up  and  especially  in  a  chain  of  reasoning, 
in  extended  phrases,  so  as  to  escape  ready  detection. 

§  122.  In  the  Disjunctive  Syllogism,  the  Law  of  perfect 
thought  requires  — 

1°.  That  the  disjunction  in  the  Sumption  be  verified,  and 
if  it  be  in  the  terms  or  in  contrary  opposition  by  reduction 
to  strictly  logical  contradiction. 

2°.  That  the  Conclusion  always  be  in  quality  opposed  to 
the  Subsumption,  and  have  for  its  predicate  the  disjunct 
member  not  subsumed. 

In  application  of  this  principle  of  method,  the  chief  dif- 
ficulty will  He  in  reducing  the  opposition  to  strict  logical 
contradiction.  The  most  fallacious  form  of  this  reasoning 
is,  perhaps,  where  there  is  true  opposition,  but  it  lies  in 
the  terms,  the  matter,  not  in  the  thought ;  as,  A  is  B  or 
non-B.     But  it  is  unnecessary  to  add  here  to  what  has  been 


204  PURE  LOGIC. 

already  said  of  this  distinction,  which  has  been  overlooked 
even  b}r  logicians  generally. 

§  123.  In  the  Hypothetico-Disjunctive  Syllogism  or  the 
Dilemma,  the  Law  of  perfect  thought  requires  — 

1°.  That  the  antecedent  be  verified,  in  respect  both  to  the 
disjunction  and  the  hypothetical  judgment  in  the  Sumption, 
and,  also,  in  respect  to  the  positing  or  the  sublation  in  the 
Subsumption. 

2°.  That  the  Conclusion  sublate  the  antecedent  member  of 
the  Sumption,  or  posit  the  Consequent,  and  not  conversely. 

A  fallacy  in  this  process  of  reasoning  has  become  quite 
famous.  There  are  two  accounts,  the  Greek  and  the  Roman. 
"  The  Roman  account  is  given  us  by  Aulus  Gellius,  and  is 
there  told  in  relation  to  an  action  between  Protagoras,  the 
prince  of  the  Sophists,  and  Euathlus,  a  young  man,  his  dis- 
ciple. The  disciple  had  covenanted  to  give  his  master  a 
large  sum  to  accomplish  him  as  a  legal  rhetorician ;  the  one 
half  of  the  sum  was  paid  down,  and  the  other  was  to  be  paid 
on  (he  day  when  Euathlus  should  plead  and  gain  his  first 
cause.  But  when  the  scholar,  after  the  due  course  of  pre- 
paratory instruction,  was  not  in  the  same  hurry  to  commence 
pleader  as  the  master  to  obtain  the  remainder  of  his  fee, 
Protagoras  brought  Euathlus  into  court,  and  addressed  his 
opponent  in  the  following  reasoning:  '  Learn,  most  foolish  of 
young  men,  that  however  matters  may  turn  up  —  whether  the 
decision  to-day  be  in  your  favor  or  against  you  —  pay  me  my 
demand  you  must.  For  if  the  judgment  be  against  you,  I 
shall  obtain  the  fee  by  decree  of  the  court ;  and  if  in  your 
favor,  I  shall  obtain  it  in  terms  of  the  compact,  by  which  it 
became  due  on  the  very  day  you  gained  your  first  cause. 
You  thus  must  fail,  either  by  judgment  or  by  stipulation.'  To 
this  Euathlus  rejoined  :  '  Most  sapient  of  masters,  learn  from 
your  own  argument,  that  whatever  may  be  the  finding  of  the 
court,  absolved  I  must  be  from  any  claim  by  you.  For  if 
the  decision  be  favorable,  I  pay  nothing  by  the  sentence  of 
the  judges  ;  but  if  unfavorable,  I  pay  nothing  in  virtue  of  the 


METHODOLOGY  OF  REASONINGS.  205 

compact,  because,  though  pleading,  I  shall  not  have  gained 
my  cause.  The  judges,  says  Gellius,  unable  to  find  a  ratio 
decidendi,  adjourned  the  case  to  an  indefinite  day,  and  ulti- 
mately left  it  undetermined.  A  parallel  story  is  told,  among 
the  Greek  writers,  of  the  rhetorician  Corax,  anglice  Crow, 
and  his  scholar  Tisias.  In  this  case,  the  judges  got  off  by 
delivering  a  joke  against  both  parties,  instead  of  a  decision 
in  favor  of  either.  We  have  here,  they  said,  the  plaguy 
egg  of  a  plaguy  crow  ;  and  from  this  circumstance  is  said 
to  have  originated  the  Greek  proverb,  kclkov  ko/dcikos  kokov 

tDOV. 

The  fallacy  in  the  reasoning  of  Protagoras  lies  in  the  am- 
biguity of  the  second  member  of  his  disjunction,  that  if 
Euathlus  won  the  suit,  the  money  would  be  due  by  the  terms 
of  the  compact ;  it  would  become  due  only  after  the  decision, 
and  by  virtue  of  it.  The  fallacy  in  the  reply  of  Euathlus, 
lies  also  in  a  similar  ambiguity  in  the  second  member  of  his 
disjunction,  that  the  decision  of  the  court  reached  to  a  claim 
that  would  arise  only  on  the  event  of  that  decision.  Before 
the  decision  Protagoras  had  no  claim,  and  of  course  must  lose 
his  suit ;  on  losing  his  suit,  his  claim  emerged  to  full  valid- 
ity, and  after  that  could  be  enforced.  In  both  reasonings 
there  is  thus  the  fallacy  of  substituting  in  the  conclusion  a 
different  claim  from  that  which  is  presented  equivocally  in 
the  antecedent :  in  the  one,  a  claim  before  the  decision  of 
the  case,  in  the  other  a  claim  coming  to  be  only  after  the 
decision. 

§  124.  In  the  Polysyllogism,  whether  Epichirema  or  So- 
rites, we  have  only  to  verify  the  several  links  of  the  chain, 
both  objectively  and  subjectively,  as  in  any  case  of  composite 
reasoning,  at  the  same  time  attending  to  the  consecution  of 
the  thought  that  that  be  ever  legitimate.  In  categorical 
reasonings  the  attention  will  be  chiefly  directed  to  the  middle 
term,  to  see  that  there  be  a  true  middle  in  every  separate 
link  of  the  chain  ;  and  to  the  carrying  forward  of  the  same 
judgment  from  the  place  of  conclusion  in  one  link  to  that  of 


206  PURE  LOGIC. 

antecedent  in  the  next.  In  conditional  reasonings,  in  like 
manner,  the  attention  should  be  chiefly  directed  to  the  medi- 
ating judgments,  and  then  to  the  carrying  forward  of  the  con- 
clusions in  the  several  links. 


PURE    LOGIC. 

PART  III. 

LOGICAL  PRAXIS. 

< 

CHAPTER  L 

I.   EXERCISES    IN    JUDGMENTS. 

Exercise  1.  Judgments  to  be  severally  discriminated  as 
to  — 

1.  Quality :  whether  Affirmative,  Negative,  or  Disjunct- 
ive ; 

2.  Modality  :  whether  Assertory,  Problematical,  or  Neces- 
sary ; 

3.  Degree  of  Identity :  whether  Total  or  Partial ; 

4.  Nature  of  Terms  :  whether  Categorical  or  Hypothetical ; 

5.  Logical  Quantity :  whether  Comprehensive  or  Exten- 
sive; 

6.  Nature  of  Whole :  whether  Integrate,  Substantial,  or 
Causal ;  and  the  parts  of  the  Sentence  respectively  contain- 
ing the  Terms  and  the  Copula  to  be  indicated. 

Models.  —  The  Judgment  Man  is  mortal,  is  Affirmative,  Assert- 
ory, Partial,  Categorical,  Comprehensive,  Substantial ;  the  Judg- 
ment, Alexander  may  not  have  practiced  what  he  had  learned  of  his  teach- 
er, is  Negative,  Problematical,  Partial,  Categorical,  Comprehensive, 
Causal.  The  Judgment,  If  Alexander  had  been  a  consistent  disciple  of 
Aristotle,  he  would  have  rxded  his  appetites,  is  an  Affirmative,  Assertory, 
Partial,  Hypothetical,  Comprehensive,  Causal  Judgment.  If  Alex- 
ander had  ruled  his  ambition,  he  would  either  have  made  no  conquests  or 


208  PURE  LOGIC. 

have  maintained  them,  is  a  Disjunctive,  Assertory,  Partial,  Hypotheti- 
cal, Comprehensive,  Causal  Judgment. 

1.  Iron  is  magnetic. 

2.  Iron  is  not  soluble  in  water. 

3.  Iron  either  is  magnetic  or  is  not  magnetic. 

4.  Iron  must  be  magnetic. 

5.  If  iron  be  magnetic,  it  has  polarity. 

6.  Iron  is  a  metal. 

7.  Iron  nourishes  plants. 

8.  Steel  is  carbonized  iron. 

9.  Thought  is  a  cognition. 

10.  Thought  is  a  relative  cognition. 

11.  Thought  either  is  a  mediate  cognition  or  is  an  imme- 
diate cognition. 

12.  If  thought  is  a  mediate  cognition,  it  is  beyond   its 
province  to  account  for  its  object. 

13.  Logic  is  the  science  of  necessary  thought. 

14.  Logic  methodizes  knowledge. 

15.  Logic  contains  the  doctrine  of  elements  and  the  doc- 
trine of  method. 

16.  If  logic  is  the  doctrine  of  thought,  it  is  the  necessary 
guide  to  all  intelligent  and  certain  thinking. 

17.  Thought  does  not  amplify  the  matter  of  knowledge. 

18.  Thought  either  creates  all  truth  or  creates  no  truth. 

19.  Truth  is  knowledge  of  things  as  existing. 

20.  The  knowledge  of  things  as  existing  is  relative  cog- 
nition. 

21.  The  elements  of  thought  are  judgments,  concepts,  and 
reasonings. 

22.  A  cognition  is  either  relative  or  irrelative. 

Exercise  2.   Disjunctives  in  Contrary  Opposition  to  be 
reduced  to  Contradictory  Opposition. 

Model.  —  Angles  are  right  or  not  right;  as  not  right  they  are 
acute  or  not  acute,  that  is,  obtuse. 

1.  Angles  are  right,  acute,  or  obtuse. 


EXERCISES   IN  JUDGMENTS.  209 

2.  Triangles  are  equilateral,  isosceles,  or  scalene. 

3.  A  quadrilateral  figure  is  either  a  square,  an  oblong,  a 
rhombus,  a  rhomboid,  or  a  trapezium. 

4.  Bodies  are  in  stable,  in  unstable,  or  in  indifferent  equi- 
librium. 

5.  A  body  will  be  supported  if  the  point  of  support  be 
applied  at,  below,  or  above  the  center  of  gravity. 

6.  A  body  is  at  rest,  in  relative  motion,  or  in  absolute 
motion. 

7.  Motion  is  either  horizontal,  perpendicular,  inclined,  or 
rotary. 

8.  Winds  are  constant,  periodical,  or  variable. 

9.  Mirrors  are  plane,  convex,  or  concave. 

10.  The  kingdoms  of  nature  are  the  mineral,  the  vegeta- 
ble, and  the  animal  kingdom. 

11.  A  carnivorous  animal  either  walks  on  the  sole  as  man, 
on  the  toes  as  the  dog,  or  is  amphibious  as  the  seal. 

12.  A  ruminant  animal  is  either  horned  like  the  ox,  or  a 
camel  or  a  llama. 

13.  The  thick-skinned  order  of  animals  either  have  trunks 
like  the  elephant,  or  have  no  trunks  like  the  swine,  or  are 
single-hoofed  like  the  horse. 

14.  He  is  either  standing,  or  sitting,  or  lying. 

15.  The  color  is  blue,  or  yellow,  or  red. 

16.  Attention  is  either  purely  spontaneous,  prompted  by 
desire,  or  voluntary. 

17.  Space  is  finite,  infinite,  or  ideal. 

18.  A  judgment  is  either  affirmative,  or  negative,  or  dis- 
junctive. 

19.  The  world  is  either  eternal,  or  the  result  of  chance, 
or  the  work  of  an  intelligent  Creator. 

20.  The  virtues  are  either  passions,  faculties,  or  habits. 

21.  The  languages  are  either  monosyllabic,  agglutinative, 
or  inflectional. 

Exercise  £.  (1.)  Judgments,  the  Modality  of  which  is  to 
14 


210  PURE  LOGIC. 

be  changed  ;  as  from  Problematic  to  Assertory  and  Apodictic, 
and  the  reverse. 

1.  It  may  rain  to-morrow. 

2.  It  is  possible  that  Encke's  comet  will  appear  again  in 
three  and  a  third  years. 

3.  There  may  have  been  such  a  character  as  the  Wander- 
ing Jew. 

4.  Such  a  rain  must  have  been  accompanied  by  atmos- 
pheric movements  of  great  violence. 

5.  Judicious  exercise  must  invigorate. 

6.  No  man  can  know  that  he  reasons  soundly  who  does 
not  know  something  of  the  laws  of  thought. 

7.  No  possible  benefit  can  result. 

8.  Alexander  possibly  conquered  Darius. 

9.  Integrity  will  certainly  reap  its  reward. 

10.  Two  wrongs  cannot  make  one  right. 

(2.)  Propositions,  the  Modality  in  which  is  to  he  discrirm- 
tiated,  whether  in  the  Copida  or  the  Terms  ;  or  if  equivocal, 
the  ambiguity  to  be  removed. 

1.  He  is  a  possible  witness. 

2.  No  merely  probable  issue  will  justify  the  adventure. 

3.  A  relapse  is  possible. 

4.  The  relation  between  cause  and  effect  is  a  necessary 
relation. 

5.  He  must  go  ;  the  command  is  peremptory. 

6.  No  possible  good  can  result. 

7.  Perhaps  he  will  succeed. 

8.  It  necessarily  comes  about  that  we  are  here  to-day. 

9.  Altogether  unnecessary  is  all  this  display. 

10.  Life  must  end  soon. 

Exercise  4.  Partial  Judgments  to  be  explicated  so  as  to 
show  the  Parts  of  the  Terms  which  are  identified. 

Model. — One  of  the  characters  that  make  up  the  concept,  man, 
is  identical  with  mortal ;  man  is  one  of  the  parts  that  make  up  the 
class  biped.  • 


EXERCISES  IN  JUDGMENTS.  211 

1.  Man  is  mortal. 

2.  Man  is  a  mortal. 

3.  Man  is  two-footed. 

4.  Man  is  a  biped. 

5.  Bucephalus  is  one-hoofed. 

6.  Bucephalus  is  a  quadruped. 

7.  A  judgment  is  a  product  of  thought. 

8.  A  judgment  is  an  act  of  thought. 

9.  A  judgment  is  thought. 

10.  The  judgment  is  correct. 

11.  The  judgment  is  partial. 

12.  The  proposition  is  complex. 

13.  The  proposition  is  true. 

14.  Virtue  is  voluntary. 

15.  Veracity  is  a  virtue. 

16.  Veracity  is  voluntary. 

17.  Whatever  is  moral  is  voluntary. 

18.  Every  voluntary  act  is  moral. 

Exercise  5.     Hypothetical  Judgments  to  he  explicated. 

Models. —In  the  Hypothetical,  If  I  think  I  am,  the  Judgment 
that  I  think  involves  the  Judgment  that  I  am,  as  action  is  part  of  being 
as  cause.  In  the  Hypothetical,  If  virtue  is  voluntary,  vice  is  voluntary, 
the  Judgment  that  virtue  is  voluntary  involves  the  Judgment  that 
vice  is  voluntary,  as  virtue  is  the  complementary  part  of  vice. 

1.  If  one  dozen  dozen  are  twelve  dozen,  half  a  dozen 
dozen  are  six  dozen. 

2.  If  one  acre  contains  one  hundred  and  sixty  square  rods, 
one  fourth  of  an  acre  contains  forty  rods. 

3.  If  the  world  were  eternal,  there  would  be  records  prior 
to  the  Mosaic. 

4.  If  the  English  are  Anglo-Saxons,  they  are  Caucasians. 

5.  If  I  think,  I  am. 

6.  If  the  universe  exhibit  design,  it  is  the  work  of  intel- 
ligence. 

7.  If  a  digestive  cavity  marks  an  animal,  the  polyp  ia  an 
animal. 


212  PURE  LOGIC. 

8.  If  matter  is  entirely  inert,  there  is  a  higher  moving 
power. 

9.  If  we  cannot  help  an  evil,  we  should  not  fret  about  it. 

10.  If  we  can  help  an  evil,  we  should  not  fret  about  it. 

Exercise  6.  Judgments  to  be  explicated  in  Comprehensive 
and  also  in  Extensive  Quantity. 

1.  Man  is  rational. 

2.  Glass  is  brittle. 

3.  Gold  is  ductile. 

4.  Thought  is  spiritual. 

5.  Passion  is  catching. 

6.  Ignorance  is  degrading. 

7.  To  lie  is  cowardly. 

8.  To  be  ungrateful  is  base. 

9.  To  die  is  to  sleep. 

10.  To  be  an  Athenian  is  to  dare. 

11.  That  we  still  breathe  is  of  mercy. 

12.  That  God  reigns  is  truth  of  richest  comfort. 

13.  Wisdom  is  no  inheritance. 

Exercise  7.  Judgments  in  Integrate,  Substantial,  and 
Causal  Wholes  to  be  discriminated,  explicated,  and,  when 
necessary,  corrected. 

1.  The  surface  of  a  square  is  double  that  of  a  triangle 
on  the  same  base  and  of  the  same  height. 

2.  A  whole  is  equal  to  the  sum  of  its  parts. 

3.  A  square  is  equal  to  the  sum  of  the  squares  of  any  two 
parts  into  which  it  may  be  divided,  together  with  double  the 
rectangle  of  its  parts. 

4.  A  whole  contains  each  of  its  parts. 

5.  The  solar  system  contains  the  sun,  planets,  and  their 
satellites. 

6.  The  body  consists  of  solids  and  fluids. 

7.  Atmospheric  air  is  composed  of  oxygen  and  nitrogen. 

8.  Water  consists  of  oxygen  and  hydrogen. 


EXERCISES   IN  JUDGMENTS.  213 

9.  Percussion  is  a  combination  of  friction  and  compression. 

10.  A  square  is  rectangular. 

11.  The  sun  is  luminous. 

12.  The  atmosphere  has  weight. 

13.  Europe  is  temperate. 

14.  Fire  burns. 

15.  The  wood  burns. 

16.  The  bellman  rings. 

17.  The  bell  rings. 

18.  The  sun  illuminates  the  earth. 

19.  The  earth  reflects  the  light  of  the  sun. 

20.  Vulgar  eyes  judge  rather  by  the  event  than  by  the 
intention. 

21.  Fortunate  is  better  than  wise. 

22.  The  mind's  excellency  can  solve  the  real  blemishes  of 
the  body. 

Exercise  8.  Propositions  to  be  corrected,  with  indication 
of  the  particular  imperfection,  whether  in  respect  of  Matter^ 
of  Judgment,  or  of  Expression. 

1.  Triangles  are  either  equilateral  or  equi-angular. 

2.  Triangles  are  right-angled,  isosceles,  or  scalene. 

3.  All  that  glitters  is  not  gold. 

4.  The  gods  of  the  heathen  are  no  gods. 

5.  No  God  is  worshiped  there. 

6.  Not  all  the  ills  of  earth  can  mar  my  joy. 

7.  Some  prudence  is  commendable. 

8.  We  do  not  admit  a  possible  failure  into  our  plans. 

9.  A  bold  front  must  win  for  us. 

10.  Animal  body  is  composed  of  flesh,  bones,  and  muscles. 

11.  The  atmospheric  air  is  made  up  of  oxygen,  nitrogen, 
cai'bonic  acid,  and  electricity. 

12.  Root,  trunk,  bark,  and  branches  form  the  tree. 

13.  Embryos  in  pines  are  radicles  or  stemlets. 

14.  Every  chemical  substance  has  combining  or  equivalent 
members. 


21'4  PURE  LOGIC. 

15.  Simple  bodies  are  divided  into  two  classes,  metals  and 
metalloids,  or  non-metallic  elements. 

16.  Leaves  are  opposite  or  alternate. 

17.  The  eastern  winds  here  are  winds  that  blow  from  the 
tropics  or  trades. 

18.  Oxygen  forms  with  silicon  silica  or  silicic  acid. 

19.  Of  spiry  or  spire-shaped  trees,  the  firs  or  spruces  are 
the  best  illustrations. 

II.   EXERCISES   IN    CONCEPTS. 

Exercise  9.  Concepts  to  be  defined  ;  to  be  analyzed,  also, 
both  by  Division  and  Partition. 

1.  Animal.  2.  The  Lynx.  3.  The  Beaver.  4.  The 
Armadillo.  5.  The  Zebra.  6.  The  Dromedary.  7.  The 
Reindeer.  8.  The  Antelope.  9.  The  Dolphin.  10.  The 
Eagle.  11.  The  Thrush.  12.  The  Linnet.  13.  The  Spar- 
row. 14.  The  Jay.  15.  The  Hoopoe.  16.  The  Lapwing. 
17.  The  Flamingo.  18.  The  Pelican.  19.  The  Teal.  20. 
The  Basilisk.  21.  The  Chameleon.  22.  The  Cobra  Ca- 
pello.  23.  The  Salamander.  24.  The  Flying-Fish.  25. 
The  Torpedo.  26.  The  Argonaut.  27.  The  Lobster.  28. 
The  Tarantula.  29.  The  Cochineal.  30.  The  Thistle  Bird. 
31.  The  Violet.  32.  The  Pomegranate.  33.  The  Cypress. 
34.  The  Amethyst.  35.  The  Emerald.  36.  Topaz.  37. 
Heat.  38.  Crystal.  39.  Carbon.  40.  Mercury.  41.  Oxyd. 
42.  Monsoon.  43.  Botany.  44.  Grammar.  45.  Psychology. 
46.  Intellect.  47.  Virtue.  48.  Hope.  49.  Purpose.  50. 
Habit.  51.  State.  52.  Church.  -  53.  Government.  54. 
Money.  55.  Art.  56.  Industry.  57.  Agriculture.  58. 
Ship.     59.  Navy.     60.  Judiciary. 

III.    EXERCISES   IN   REASONINGS. 

Observation. — As  the  movements  of  Thought  in  ordinary  dis- 
course are  abbreviated  and  complicated,  it  is  necessary,  in  order  to 
verify  them,  to  reduce  them  to  their  full  logical  form  in  their  several 
distinct  elements.  In  order  to  this,  it  will  be  found  convenient  to 
separate  the  Terms,  and  mark  them  by  familiar  signs,  as  W,  P,  and 


EXERCISES  IN  REASONINGS.  215 

M,  for  Major,  Minor,  and  Middle  Terms,  respectively,  and  to  place 
the  Judgments  in  a  fixed  order,  the  antecedent  with  its  Sumption 
and  Subsumption,  if  it  be  a  Mediate  Reasoning,  above,  and  the  con- 
sequent below.  Begin  with  the  conclusion  ;  mark  the  Terms  as  W 
and  P  respectively ;  then  find  the  Middle  Term  or  Terms,  and  con- 
struct the  Sumption  and  the  Subsumption.  The  reasoning  will  then 
be  readily  recognized  as  valid  or  not  by  the  application  of  the  Rules 
of  Reasoning. 

Exercise  10.     Complex  Reasonings  to  he  resolved. 

1.  All  poets  are  men  of  genius;  therefore,  some  men  of 
genius  are  poets. 

2.  He  who  is  content  with  what  he  has,  is  truly  rich ;  a 
covetous  man  is  not  content  with  what  he  has  ;  therefore,  no 
covetous  man  is  truly  rich. 

3.  All  the  righteous  are  happy ;  therefore,  all  who  are 
unhappy  are  unrighteous. 

4.  All  insincere  men  are  dishonest ;  therefore,  all  honest 
men  are  sincere. 

Exercise  11.  Reasonings  with  suppressed  Premises  to  be 
supplied. 

1.  All  tyrants  deserve  death ;  therefore,  Caesar  deserved 
death. 

2.  "Whatever  comes  from  God  is  entitled  to  reverence ; 
therefore,  the  Scriptures  are  entitled  to  reverence. 

3.  Of  two  evils,  the  less  is  to  be  preferred ;  occasional 
turbulence,  therefore,  is  to  be  preferred  to  rigid  despotism. 

4.  Wine  is  hurtful ;  for  all  stimulants  are  hurtful. 

5.  An  infant  has  no  moral  power;  therefore,  it  has  no 
responsibility. 

6.  Kings  have  no  friends ;  for  they  have  no  equals. 

7.  The  lion  is  a  predaceous  animal ;  therefore,  it  is  not 
ruminant. 

8.  Innate  ideas  cannot  be  enumerated  ;  therefore,  they  do 
not  exist. 

9.  Solon  was  a  wise  legislator ;  for  he  suited  his  laws  to 
the  genius  of  his  nation. 


216  PURE  LOGIC. 

10.  The  Epicureans  cannot  be  regarded  as  true  philoso- 
phers ;  for  they  did  not  reckon  virtue  a  good  in  itself. 

11.  Shame  is  not  a  virtue  ;  for  it  is  more  a  passion  than  a 
habit. 

12.  Gambling  implies  a  desire  to  gain  by  another's  loss  j 
therefore,  it  is  a  violation  of  the  tenth  commandment. 

13.  Onesimus  was  a  servant  of  Philemon  ;  Philemon  was 
a  hearer  of  Archippus  ;  Archippus  was  a  minister  at  Colosse ; 
therefore,  Onesimus  was  a  resident  at  Colosse. 

14.  The  nervous  fluid  is  not  electricity ;  for  electricity 
may  be  transmitted  along  a  nervous  trunk  which  has  been 
compressed  by  a  string  tied  tightly  round  it,  whilst  the  pas- 
sage of  ordinary  nervous  power  is  as  completely  checked  by 
this  process  as  if  the  nerve  had  been  divided. 

Exercise  12.  Reasonings  to  he  discriminated  as  to  their 
nature,  as  Immediate,  Categorical,  or  Conditional,  with  indi- 
cation of  Mediating  Judgments  in  the  latter,  and  Middle 
Terms  in  Categorical  Syllogisms. 

1.  Equilateral  triangles  are  equi-angular  ;  therefore,  equi- 
angular triangles  are  equilateral. 

2.  Government  is  either  a  property  or  a  trust ;  it  is  not 
a  property ;  it  must,  therefore,  be  a  trust. 

3.  If  there  were  no  divine  Providence,  no  human  govern- 
ment could  long  subsist ;  various  human  governments  have 
subsisted  long ;  therefore,  there  must  be  a  divine  Provi- 
dence. 

4.  The  early  and  general  assignment  of  the  Epistle  to  the 
Hebrews  to  the  Apostle  Paul  as  its  author,  must  have  been 
either  from  its  professing  to  be  his,  or  from  its  really  being 
his  ;  but  it  does  not  profess  to  be  his  ;  therefore,  it  is  really 
his. 

5.  No  person  can  serve  God  and  mammon ;  the  covetous 
man  serves  mammon ;  he  cannot,  therefore,  serve  God. 

6.  If  the  prophecies  of  the  Old  Testament  had  been  written 
without  knowledge  of  the  events  of  the  time  of  Christ,  they 


EXERCISES  IN  REASONINGS.  217 

could  not  have  corresponded  with  them  exactly  ;  and  if  they 
had  been  forged  by  Christians,  they  would  not  be  preserved 
and  acknowledged  by  the  Jews  :  but  they  did  correspond 
with  those  events,  and  they  are  preserved  and  acknowledged 
by  the  Jews  ;  therefore,  they  were  neither  written  without 
knowledge  of  those  events,  nor  were  they  forged  by  Chris- 
tians. 

7.  The  favor  of  God  must  be  bestowed  either  with  respect  to 
men's  persons  or  with  respect  to  their  conduct ;  but  "  God  is 
no  respecter  of  persons ;  "  therefore,  his  favor  must  be  be- 
stowed with  respect  to  men's  conduct. 

8.  If  any  complete  theory  could  be  framed  to  explain  the 
establishment  of  Christianity  by  human  causes,  such  a  theory 
would  have  been  proposed  before  now ;  but  no  such  theory 
ever  has  been  prepared  ;  therefore,  none  can  be  framed. 

9.  If  the  system  of  the  universe  is  not  the  best  possible,  we 
must  suppose  either  that  the  Creator  did  not  prefer  a  better 
one,  or  that  be  knew  no  better  one,  or  that  he  could  not 
create  a  better ;  but  we  can  entertain  neither  of  these  sup- 
positions, for  we  should  thereby  limit  his  goodness,  his  intel- 
ligence, or  his  power  ;  therefore,  the  system  of  the  universe 
is  the  best. 

Exercise  13.     Fallacies  to  be  detected. 

"  By  discourse,"  says  Chillingworth,  meaning  by  the  word  the 
operation  of  the  discursive  faculty,  or  Thought,  "  no  man  can  possibly 
be  led  into  error ;  but  if  he  err  in  his  conclusions,  he  must  of  neces- 
sity either  err  in  his  principles  or  commit  some  error  in  his  discourse  ; 
that  is,  indeed,  not  discourse  but  seem  to  do  so." 

1.  All  men  are  mortal ;  therefore,  all  mortals  are  men. 

2.  No  man  is  infallible  ;  therefore,  every  fallible  being  is 
human. 

3.  All  men  are  not  virtuous ;  therefore,  all  men  are 
vicious. 

4.  All  unjust  acts  should  be  punished ;  therefore,  all  acts 
not  punished  should  be  just. 


218  PURE  LOGIC. 

5.  No  evil  should  be  allowed  that  good  may  come  of  it ; 
all  punishment  is  an  evil ;  therefore,  no  punishment  should 
be  allowed  that  good  may  come  of  it. 

6.  A  problem  is  neither  affirmative  nor  negative ;  every 
proposition  is  either  affirmative  or  negative ;  therefore,  a 
problem  is  not  a  proposition. 

7.  An  enslaved  people  are  not  happy  ;  the  English  people 
are  not  enslaved  ;  therefore,  the  English  are  happy. 

8.  None  but  whites  are  civilized ;  the  'ancient  Germans 
were  whites  ;  therefore,  they  were  civilized. 

9.  If  it  is  our  duty  now  to  love  our  neighbor,  it  was  our 
duty  to  love  him  before  he  was  born  ;  for  the  law  of  duty  is 
unchangeable. 

10.  Change  is  agreeable ;  death  is  a  change ;  therefore, 
death  is  agreeable. 

11.  Those  who  work  hard  deserve  reward;  those  who 
work  .on  the  treadmill  wrork  hard ;  therefore,  they  deserve 
reward. 

12.  "  No  nation,"  says  Earl  Russell,  in  his  speech  in  Par- 
liament, March  23d,  1865,  "  has  a  right  to  blockade  one  of 
its  own  ports  when  seized  by  insurgents,  without  recognizing 
such  insurgents  as  belligerents  ;  "  therefore,  Irish  insurgents 
seizing  any  port  in  Ireland  have  a  right  to  open  commerce  or 
to  be  recognized  as  belligerents. 

13.  No  one  who  lives  on  terms  of  confidence  with  another 
has  a  right  in  any  circumstances  to  take  his  life;  Brutus 
lived  on  terms  of  confidence  with  Caesar ;  therefore,  he  had 
no  rio;ht  to  take  his  life. 

14.  He  that  destroys  an  usurper,  does  right;  Brutus 
destroyed  an  usurper  ;  therefore,  he  did  right. 

15.  None  can  perform  impossibilities ;  miracles  are  im- 
possibilities ;  therefore,  none  can  perform  miracles. 

16.  A  story  is  not  to  be  believed,  the  reporters  of  which 
give  contradictory  accounts  ;  the  story  of  Bonaparte  is  con- 
tradictorily reported  ;  therefore,  it  ought  not  to  be  believed. 

17.  That  which  requires  self-denial  is  not  habitual ;  all 


EXERCISES  IN  REASONINGS.  219 

virtue  requires  self-denial ;  therefore,  no  virtue  can  be  hab- 
itual. 

18.  Have  you  the  ten  marbles  I  gave  you  ?  No  ;  I  have 
not  ten,  for  I  have  lost  three.  Have  you  lost  all  that  you 
have  not  got  ?     Yes.     Then  you  must  have  lost  ten. 

19.  Do  you  know  what  I  am  to  ask?  No.  Then  you  do 
not  know  whether  fish  is  fowl ;  for  that  is  what  I  was  to  ask. 

20.  Do  you  know  who  that  is  in  the  street  yonder  ?  No. 
Then  you  do  not  know  your  own  father. 

21.  Does  one  grain  of  corn  make  a  heap  ?  No.  Do  two? 
No.  Three  ?  No.  Nine  hundred  and  ninety-nine  ?  No. 
One  thousand  ?  Yes.  Then  one  grain  makes  the  difference 
between  a  heap  and  no  heap. 

22.  Have  you  cast  your  horns?  No.  Then  you  must 
have  them  still. 

23.  Can  a  body  move  where  it  is  not  ?  No.  Can  a  body 
move  if  it  continue  where  it  is  ?  No.  Then  a  body  cannot 
move  at  all,  for  it  must  move  where  it  is  or  where  it  is  not. 

24.  Can  a  cause  act  except  where  it  is  ?  No.  Then  how 
can  the  sun  cause  heat  on  the  earth  ? 

25.  Every  man  is  an  animal ;  a  swan  is  not  a  man ;  there- 
fore, no  swan  is  an  animal. 

26.  No  man- is  inanimate;  snow  is  not  man;  therefore, 
snow  is  not  inanimate. 

27.  A  horse  may  be  white ;  snow  is  not  a  horse  ;  there- 
fore, snow  is  not  white. 

28.  Honey  is  yellow ;  gall  is  yellow ;  therefore,  gall  is 
honey. 

29.  He  who  is  silent  cannot  speak  ;  John  is  silent ;  there- 
fore, John  cannot  speak. 

30.  The  wise  are  good ;  some  ignorant  people  are  good ; 
therefore,  some  ignorant  people  are  wise. 

31.  Animal  food  may  be  entirely  dispensed  with,  for  the 
Brahmins  live  without  it ;  and  vegetable  food  may  be  dis- 
pensed with,  for  the  Esquimaux  live  without  it  :  but  all 
food  consists  of  animal  food  and  vegetable  food ;  therefore, 
all  food  may  be  dispensed  with. 


220  PURE  LOGIC. 

32.  In  a  perfect  vacuum,  nothing  can  be  supposed  to  be ; 
therefore,  in  a  perfect  vacuum  there  can  be  no  motion. 

33.  No  one  desires  evil,  knowing  it  to  be  so ;  to  do  wrong 
is  evil ;  therefore,  no  one  desires  to  do  wrong  except  in  igno- 
rance. 

34  The  action  of  living  organism  is  vital  action  ;  a  fever 
is  action  of  living  organism ;  therefore,  a  fever  is  vital 
action. 

35.  No  trifling  business  will  enrich  those  engaged  in  it ;  a 
mining  speculation  is  no  trifling  business  ;  therefore,  it  will 
enrich  whoever  engages  in  it. 

36.  He  who  is  most  hungry  eats  most ;  he  who  eats  least 
is  most  hungry  ;  therefore,  he  who  eats  least  eats  most. 

37.  He  who  calls  you  a  man  speaks  truly ;  he  who  calls 
you  a  poet  calls  you  a  man ;  therefore,  he  who  calls  you  a 
poet  speaks  truly. 

38.  Nothing  is  heavier  than  platina  ;  feathers  are  heavier 
than  nothing ;  therefore,  feathers  are  heavier  than  platina. 

39.  All  cold  is  to  be  expelled  by  heat ;  this  man's  disorder 
is  a  cold ;  therefore,  it  is  to  be  expelled  by  heat. 

40.  What  we  eat  grew  in  the  fields  ;  loaves  of  bread  are 
what  we  eat ;  therefore,  loaves  of  bread  grew  in  the  field. 

41.  We  eat  what  we  buy  in  the  market  j  we  buy  in  the 
market  raw  meat ;  therefore,  we  eat  raw  meat. 

42.  Jupiter  is  next  to  Mars ;  Saturn  is  next  to  Jupiter ; 
therefore,  Saturn  is  next  to  Mars. 

43.  If  Aristotle  was  infallible,  Logic  is  worthy  of  being 
cultivated  ;  but  Aristotle  was  not  infallible ;  therefore,  Logic 
is  unworthy  of  being  cultivated. 

44.  If  the  Mosaic  Law  was  designed  only  for  Hebrews, 
the  worship  of  images  is  not  forbidden  to  Christians ;  but  it 
was  not  designed  only  for  Hebrews ;  therefore,  the  worship 
of  images  is  forbidden  to  Christians. 

45.  Every  thing  that  exists,  exists  in  space ;  but  space 
does  not  exist  in  space ;  therefore,  space  does  not  exist. 

46.  All  rules  have  exceptions ;  this  very  rule,  itself,  then, 


EXERCISES   IN  REASONINGS.  221 

that  all  rules  have  exceptions,  has  exceptions.     It  is  not  true 
then  that  all  rules  have  exceptions. 

47.  Let  9  be  represented  by  x  and  30  by  y.  Then  if  we 
take  the  self-evident  equations  ax  =  ax  and  ay  =  ay,  add 
them  together,  and  transpose  the  terms,  we  shall  have  ax — 
ax=ay—ay.    Dividing  by  a— a,  we  have  x  =  y  ;  or  9  =  30. 

Exercise  14.      Topics  for  discussion  or  investigation. 

1.  History  of  the  changes  in  meaning  of  the  term  Thought. 

2.  What  are  the  faculties  of  the  intelligence  ? 

3.  "Which  are  faculties  of  original  cognition  ? 

4.  Diversity  of  opinion  as  to  the  proper  sphere  of  Logic. 

5.  The  relationship  of  the  true,  the  beautiful,  and  the 
good. 

6.  How  much  of  truth  is  there  in  the  Hudibrastic 
couplet  — 

"  That  all  a  Rhetorician's  rales 
Serve  only  but  to  name  his  tools  "  ? 

7.  Enumerate  the  intuitions  of  the  mind. 

8.  Classify  the  possible  predicates  in  thought. 

9.  The  forms  in  which  the  subject  of  a  sentence  may  be 
expressed  in  language. 

10.  Enumerate  the  modals  or  modal  adverbs  in  current 
use  in  the  English  language. 

11.  Enumerate  the  general  classes  of  concrete  nouns  in 
language. 

12.  Enumerate  the  general  classes  of  abstract  nouns. 

13.  What  constitutes  a  species  in  the  natural  world  ? 

14.  What  is  the  difference  between  reason  and  reasoning  ? 

15.  The  meaning  of  the  word  Idea;  its  etymological  im- 
port, and  the  significance  given  it  by  Grecian,  Roman,  and 
modern  philosophers. 

16.  The  meaning  of  the  word  Intuition,  as  determined  by 
its  etymology  and  use. 

17.  The  Nominalist  controversy. 

18.  The  difference  in  meaning  between  substance  and  sub- 
ject. 


222  PURE  LOGIC. 

19.  The  difference  in  meaning  between  truth  and  reality. 

20.  The  fundamental  postulate  in  human  belief. 

21.  Belief  and  knowledge. 

22.  Can  a  concept  be  imagined  ? 

23.  Example  and  induction. 

24.  What  is  form  ? 

25.  Classification  of  the  sciences. 

26.  The  application  of  induction  to  moral  matter. 

27.  History  of  Logic. 

28.  Indian  Logic. 

29.  Law  and  general  fact. 

30.  Law  and  idea. 

31.  Identity  and  resemblance. 

32.  Js  all  inference  from  particulars  to  particulars  ? 

33.  Is  all  deduction  from  a  previous  induction  ? 

34.  Comparison  of  the  two  methods  of  advancing  science 
by  observation  :  1.  By  adding  to  the  number  of  individuals 
or  of  species  in  the  class  ;  2.  By  adding  to  the  attributes  that 
belong  to  the  class. 

35.  Importance  to  success  of  consciously  distinguishing  the 
two  methods  of  observation,  stated  above. 

36.  Advancement  of  science  by  multiplication  of  classes, 
whether  (1)  by  higher  generalizations,  or  (2)  by  lower  sub- 
divisions. 

37.  Advancement  of  science  by  observation  of  attributes, 
whether  (1)  by  discovery  of  new  attributes,  or  (2)  by  anal- 
ysis of  known  attributes  that  are  composite. 

38.  Advancement  of  science  by  observation  of  attributes, 
whether  (1)  of  properties,  or  (2)  of  relations. 


APPENDIX 


A. 

INDUCTION. 

The  proper  nature  and  function  of  Induction  as  a  process  of 
Thought  have  been  involved  in  much  confusion  and  dispute,  and, 
of  course,  in  obscurity  and  error.  To  such  extent  is  this  true  that 
Sir  William  Hamilton  does  not  hesitate  to  declare  in  unqualified 
terms  that  all  to  be  found  in  logical  treatises  on  this  subject  "  is 
utterly  erroneous."  Yet  it  is  noticeable  that  with  this  disagree- 
ment there  is  still  a  harmony  of  view  in  regard  to  the  leading 
characteristics  of  Induction,  when  they  are  regarded  separately 
from  the  special  theories  held  by  the  differing  logicians ;  which 
characteristics,  thus  separately  admitted  by  all,  or  at  least  by  the 
great  majority,  when  brought  together  and  wrought  into  system, 
make  up  a  complete  and  altogether  consistent  and  trustworthy 
doctrine  of  Induction. 

All  agree  in  admitting  Induction  to  be  a  process  of  Thought,  and 
in  regarding  all  Thought,  as  Thought,  as  properly  within  the  pur- 
view of  logical  science.  This  admission  at  once  disposes  of  the 
marvelous  error  of  Hamilton  in  rejecting  common,  material  Induc- 
tion, from  the  sphere  of  the  Science  of  Thought.  If  this  Induction 
is  not  a  process  of  Thought,  what  is  it  indeed  ?  As  well  might  he 
claim  that  engineering  calculations  do  not  come  within  the  prov- 
ince of  Arithmetical  or  of  Geometrical  Science.  We  can  as  well 
calculate  in  engineering  without  conforming  to  arithmetical  and 
geometrical  principles,  as  induce  in  Natural  Science  without  con- 
forming to  logical  principles. 

Again,  all  agree  in  regarding  Induction  as  a  reasoning  process. 
As. a  reasoning,  it  differs  from  a  concept,  inasmuch  as  the  one  ter- 
minates in  a  new  judgment,  while  the  other  results  in  an  object 


224  APPENDIX. 

of  thought  which  may  be  used  as  either  subject  or  predicate  in  a 
new  judgment ;  but  agrees  with  it  in  being  a  derivative  process 
which  gives  a  result  not  contained  in  the  several  given  judgments 
from  which  the  process  starts  as  a  datum,  if  they  are  taken  sepa- 
rated. But  it  is  a  logical  illusion  to  throw  the  result  into  the  form 
of  a  Categorical  Judgment  instead  of  a  Concept,  in  order  to  make 
it  appear  as  an  Induction.  This  disposes  of  the  theory  of  those 
who  confound  Inductions  with  Concepts,  and  who  exemplify  this 
process  thus :  Socrates  is  rational,  Plato  is  rational,  Xenophon  is 
rational ;  Socrates,  Plato,  Xenophon  are  men  ;  therefore,  men 
are  rational.  We  have  here  a  true  method  of  forming  a  con- 
cept ;  but  we  have  no  reasoning,  only  a  fantasy ;  for  we  have 
only  substituted  a  single  word  for  several  expressing  precisely  the 
same  object  of  thought.  For  evidently  if  we  have  attached  any 
other  meaning  to  men  than  what  we  mean  by  Socrates,  Plato, 
Xenophon,  either  as  to  their  Sphere  or  Extension,  or  as  to  their 
Comprehension,  the  whole  process  is  a  fallacy.  It  is  equally  illu- 
sive as  it  would  be  to  say,  Horse  is  four-footed ;  equus  is  horse ; 
therefore,  equus  is  four-footed,  and  suppose  we  have  attained  a 
new  judgment  respecting  equus  as  an  object  of  thought.  This 
theory  has  soundness  in  it  so  far  as  it  exemplifies  a  process  of 
forming  and  naming  concepts,  but  so  far  as  designed  to  exemplify 
a  reasoning,  is  merely  a  play  upon  words. 

Further,  all  agree  in  admitting  a  real  distinction  between  In- 
ductive and  Deductive  Reasoning.  This  distinction  they  recog- 
nize as  lying  in  the  direction  of  the  movement  of  the  Thought  — 
the  one  moving  from  the  Whole  as  its  starting-point,  the  other 
from  the  Part.  They  all  accept  the  following  as  an  example  of 
true  Inductive  Reasoning :  This,  that,  and  the  other  magnet  at- 
tract iron  ;  therefore,  so  do  all.  Now  this  admission  should  pre- 
clude the  attempt  to  bring  it  under  a  deductive  reasoning  with  a 
suppressed  universal  Major  Premise  or  Sumption,  as  do  Whately 
and  others,  or  under  a  deductive  reasoning  with  a  suppressed 
Minor  Premise  or  Subsumption,  as  does  Aldrich.  This  is  just  to 
contradict  their  admission  as  well  as  to  run  counter  to  the  teach- 
ing of  their  great  authority,  Aristotle,  who  expressly  teaches  that 
Induction  is  from  the  particular  or  individual,  having  apparently 
confounded  the  inductive  process  of  Aristotle  with  what  he  calls 
the  syllogism  from  induction.  Aristotle's  extant  writings  nowhere 
indicate  that  he  viewed  induction  itself  as  syllogistic,  and  so  ana- 


APPENDIX.  225 

lytic ;  on  the  other  hand,  he  ever  opposes  the  one  process  to  the 
other.l  To  suppose  Induction  to  be  an  Enthymeme  with  Major 
Premise  or  Sumption  suppressed,  is  entirely  irreconcilable  with 
such  doctrine.  This  admission  should  preclude,  also,  any  such 
fallacious  attempt  as  that  of  Hamilton  to  make  Induction  a  proc- 
ess from  all  the  parts  to  the  whole.  This  procedure  is  to  be  re- 
jected equally  with  that  which  we  have  already  exposed  as  con- 
founding the  mere  substitution  of  one  verbal  expression  for  an- 
other with  a  new  Judgment,  and  on  the  same  ground.  This  will 
be  seen  at  once  from  Hamilton's  illustration  :  "  This,  that,  and  the 
other  magnet  attract  iron ;  hut  this,  that,  and  the  other  magnet, 
etc.,  are  conceived  to  constitute  the  genus  magnet ;  therefore,  the 
genus  magnet  attracts  iron."  To  say  nothing  of  the  irregularity 
in  introducing  in  the  Subsumption  the  very  significant  etc.  into 
the  middle  term,  it  is  clear  that  the  Subsumption  is  a  merely  tau- 
tological proposition,  and  forms  no  part  of  the  reasoning  process. 
All  the  reasoning  process  has  terminated  when  we  have  added  the 
etc.  There  is  the  same  fallacious  substitution  of  a  concept-form- 
ing process  for  a  proper  reasoning  that  has  been  already  exposed. 
All  agree  in  making  the  goal  of  the  movement  of  Thought  in 
Induction  a  conclusion  which  embraces  in  its  subject  the  part 
complementary  of  that  which  formed  the  starting-point,  as  illus- 
trated in  the  example  already  given.  This,  that,  and  the  other 
magnet  attract  iron  ;  therefore,  all  magnets  attract  iron.  Of  the 
class-whole  magnet,  this,  that,  and  the  other,  forming  the  starting- 
point,  are  one  part ;  the  conclusion  evidently  embraces  with  this 
the  complement  of  the  genus.  But  with  this  harmonious  teach- 
ing so  far,  we  find  a  great  divergence  of  views  in  the  further 
exposition  of  the  result  attained  in  an  Induction.  Hamilton 
and  others,  as  has  been  shown,  represent  that  the  result  is  a 
simple  gathering  of  the  part  given  in  the  Major  Premise  with 
the  complementary  part  into  a  concept;  thus,  The  part  observed  of 
magnets  attracts  iron ;  therefore,  this  part  and  the  part  unobserved 
make  up  the  genus  magnet.  There  is  no  proper  reasoning  in  this  ; 
it  is  simply  a  naming  process  disguised  under  the  garb  of  a  reason- 
ing. Others,  as  Whately,  shun  this  error  of  Hamilton,  but  repre- 
sent the  subject  of  the  conclusion  to  be  a  genus,  including,  of 
course,  both  the  datum  and  the  complement.  Others,  as  Thomp- 
son, in  his  "  Laws  of  Thought,"  make  the  result  of  Induction  "  a 

1  See  his  Topics,  1. 10;  Prior  Analytics,  II.  25;  Rhetoric,  I.  2. 
15 


226  APPENDIX. 

Law."  But  his  Law  is  but  the  convertible  term  of  General  Fact, 
in  the  two  different  forms  in  which  we  apprehend  Being.  When, 
thus,  we  conceive  of  material  bodies  under  the  form  of  Substance, 
we  say  it  is  a  General  Fact  that  they  are  gravitating,  —  have  this 
attribute ;  when,  on  the  other  hand,  we  conceive  of  them  under 
the  form  of  Cause,  we  say  it  is  the  law  of  material  bodies  that 
they  gravitate.  Still  another  view  is  that  which,  through  misinter- 
pretation of  Aristotle,  distinguishes  Induction  from  Example  as 
different  processes  of  Thought  —  making  one  result  in  a  genus,  the 
other  in  a  part  as  subject  of  the  conclusion.  But  there  is  no  es- 
sential difference  in  the  movements  of  Thought ;  they  differ  only 
in  mere  accidents  of  form  and  occasion.  When  from  a  given  part 
we  have  induced  to  the  complementary  part,  we  have,  in  fact, 
comprehended  the  whole ;  as,  if  P  and  C  are  the  two  parts  which 
compose  the  whole  W,  then  if  what  we  know  of  P  we  have 
induced  to  be  true  of  C,  we  have  attained  what  is  true  of  P  and 
C,  and  accordingly  of  W,  for  W  is  but  P  and  C  taken  together. 

Gathering  up,  now,  the  several  teachings  of  logicians  so  far  as 
they  agree,  we  attain  the  following  results  as  the  accepted  charac- 
teristics of  Induction  :  — 

1.  It  is  a  process  of  Thought  that  is  identical  in  essential  char- 
acter in  all  those  movements  of  Intelligence  which  induce,  which 
infer  mediately  otherwise  than  by  deduction.  There  is  but  one  In- 
duction, as  there  is  but  one  Deduction  in  all  Thought. 

2.  It  is  a  reasoning,  being  a  derivative  Judgment,  not  a  Con- 
cept ;  an  inference  from  a  datum,  implying  a  new  proper  Judg- 
ment-Cognition, not  a  mere  synthesis  of  subjects  or  of  predicates 
—  that  is,  not  a  Concept. 

3.  It  is  a  mediate  reasoning,  being  derived  not  from  a  single 
Judgment,  but  from  a  plurality  of  Judgments,  related  to  each 
other  under  the  relationship  of  part  to  complementary  part  in  two 
of  their  terms  which  are  alike  related  to  the  third  or  middle  term 
as  parts  to  a  whole. 

Of  the  validity,  independent  character,  and  extensive  use  of 
this  process  of  thought,  the  following  extract  from  Mr.  John  Stu- 
art Mill's  "  Treatise  on  Logic  "  gives  a  very  satisfactory  illustra- 
tion :  — 

"  If,  from  our  experience  of  John,  Thomas,  &c,  who  once  were 
living,  but  are  now  dead,  we  are  entitled  to  conclude  that  all 
human  beings  are  mortal,  we  might,  surely,  without  any  logical 


APPENDIX.  227 

inconsequence,  have  concluded  at  once  from  those  instances  that 
the  Duke  of  Wellington  is  mortal.  The  mortality  of  John, 
Thomas,  and  company,  is,  after  all,  the  whole  evidence  we  have 
for  the  mortality  of  the  Duke  of  Wellington.  Not  one  iota  is 
added  to  the  proof  by  interpolating  a  general  proposition.  .  .  . 
Not  only  may  we  reason  from  particulars  to  particulars  without 
passing  through  generals,  but  we  perpetually  do  so  reason.  All 
our  earliest  inferences  are  of  this  nature.  From  the  first  dawn 
of  intelligence  we  draw  inferences,  but  years  elapse  before  we 
learn  the  use  of  general  language.  The  child,  who,  having  burnt 
his  fingers,  avoids  to  thrust  them  again  into  the  fire,  has  reasoned 
or  inferred,  though  he  has  never  thought  of  the  general  maxim  — 
'  Fire  burns.'  He  knows  from  memory  that  he  has  been  burnt, 
and  on  this  evidence  believes,  when  he  sees  a  candle,  that  if  he 
puts  his  finger  into  the  flame  of  it,  he  will  be  burnt  again.  He 
believes  this  in  every  case  which  happens  to  arise ;  but  without 
looking,  in  each  instance,  beyond  the  present  case.  He  is  not 
generalizing ;  he  is  inferring  a  particular  from  particulars."  Page 
125,  New  York  Edition,  1860. 


B. 

ORIGIN    OF   LANGUAGE. 

In  all  speculations  upon  the  Origin  of  Language,  the  two  ele- 
ments in  words,  the  thought-element  —  its  significance,  and  the 
sound-element,  should  most  obviously  be  kept  entirely  distinct. 
The  thought-element  must,  further,  be  regarded  as  logically  the 
antecedent,  the  occasioning,  or  prompting,  and,  so  far  at  least,  the 
determining  element ;  however  true  it  may  be  that  chronologically 
the  two  emerge  simultaneously  into  conscious  experience.  How 
the  thought-element  originates  and  changes  in  the  progress  of 
thought  and  language,  has  been  sufficiently  indicated  in  the  text, 
§  85.  The  theory  of  Max  Miiller,  as  presented  in  the  ninth  of 
his  First  Series  of  Lectures  on  Language,  that  language  origi- 
nates with  general  ideas,  "  that  names,"  to  use  his  own  language, 
"  are  all,  without  exception,  derived  from  general  ideas,"  is  there 
characterized  as  gross  error.  But  in  addition  to  the  considerations 
there  presented  in  justification  of  this  unqualified  rejection  of  the 


228  APPENDIX. 

theory,  we  may  here  present  an  exposition  of  the  fallacy  which  viti- 
ates his  whole  reasoning.  The  fallacy  lies  in  assuming  that  a  predi- 
cate is  essentially,  and,  of  course,  primitively  a  general  idea.  All 
nouns  he  teaches  "  express  originally  one  out  of  the  many  attri- 
butes of  a  thing,  and  that  attribute,  whether  it  be  a  quality  or  an 
action,  is  necessarily  a  general  idea."  "All  naming,"  he  says,  "  is 
classification,  bringing  the  individual  under  the  general."  "Ana- 
lyze," he  says  again,  "  any  word  you  like,  and  you  will  find  that 
it  expresses  a  general  idea  peculiar  to  the  individual  to  which  the 
name  belongs.  What  is  the  meaning  of  moon  ?  The  measurer. 
"What  is  the  meaning  of  sun  ?  The  begetter.  What  is  the  mean- 
ing  of  earth  ?  The  ploughed."  And  still  again,  "  The  fact  that 
every  word  is  originally  a  predicate,  that  names,  though  signs  of 
individual  conceptions,  (?)  are  all,  without  exception,  derived 
from  general  ideas,  is  one  of  the  most  important  discoveries  in  the 
science  of  language."  Now  this  assumption,  so  quietly  and  yet  so 
confidently  employed  in  this  reasoning,  is  utterly  baseless.  A 
primitive  predicate  must  have  been  an  individual  property.  A 
generic  notion  is  a  purely  artificial  notion  —  a  mere  product  of 
thought  —  a  creation  of  thinking  man.  It  could  not  exist  before 
man  thought ;  and  as  his  first  thought  was  a  judgment,  a  recogni- 
tion of  an  attribute  as  belonging  to  an  object,  that  attribute  could 
not  have  been  a  genus,  that  is,  a  thought-product.  The  learned 
lecturer  has  undoubtedly  confounded  the  actual  with  the  potential, 
the  simple  germinant  with  the  complicated  mature.  Because  moon 
means  measurer,  which  is  assumed  in  the  argument  to  be  a  primi- 
tive predicate,  he  assumes  that  it  was  so  named  because  measurer 
at  that  primitive  time  of  naming,  was  generic  —  included  a  class 
of  objects  as  then  known  in  human  speech,  for  he  is  emphatic  in 
his  teaching  that  thought  and  speech  originate  together  —  "lan- 
guage and  thought  are  inseparable."  But  all  this  is  error.  Meas- 
urer was  not  actually  generic,  but  only  potentially  so  ;  that  is,  the 
simple  attribute  of  measurer,  assuming  it  still  to  be  a  primitive 
word,  originally  applied  to  an  individual  object  —  say  the  moon, 
and  to  that  only,  was  only  afterwards,  in  the  progress  of  thought 
and  speech,  applied  to  other  objects,  as  one  after  another  they 
came  into  human  consciousness.  Only  in  this  way  did  it  come  to 
be  generic.  It  could  not  have  been  generic,  at  first,  in  the  possi- 
bilities of  human  experience  ;  it  became  so.  In  other  words,  it 
was  not  actually,  but  only  potentially  generic.     This  fundamental 


APPENDIX.  229 

fallacy  vitiates  his  whole  reasoning,  and  involves  it  in  absurdities 
all  along  his  path.  His  illustrations  to  prove  the  origin  of  words 
never  go  back  to  a  first,  but  only  to  a  prior,  which  must  itself  have 
had  a  prior.  Cave  was  named  from  the  idea  to  cover.  But  whence 
did  cover  originate  ?  Was  it  primitive  ?  Then  it  must  have  ex- 
isted before  its  class,  and,  of  course,  could  not  have  been  at  that 
time  generic.  Yet  it  is  the  origin  of  words,  the  rise  of  the  first 
words,  that  the  theory  attempts  to  explain.  So  "  all  naming,"  he 
says,  "  is  classification,  bringing  the  individual  under  the  general." 
How  then  could  the  first  naming  have  been  effected  ?  Was  the 
general  before  the  individual  which  it  includes  ?  As  "  language 
and  thought  are  inseparable,"  this  general  that  is  antecedent  to 
all  naming,  that  is,  to  all  language,  must  have  been  before  all 
thought.     When  and  what  was  it  ? 

The  question  as  to  the  origin  of  the  sound-element  in  the  word, 
how  a  particular  sound  comes  to  embody  a  notion,  what  deter- 
mines this  and  that  sound  to  this  and  that  idea,  is  a  totally  distinct 
question.  M.  Muller  in  his  lectures  mentions  three  theories.  One 
is,  that  the  roots  of  words  are  imitations  of  sounds  ;  a  second,  that 
they  are  involuntary  interjections.  These  two  theories  he  rejects, 
and  styles  them  respectively  the  Bow-wow  theory,  and  the  Pooh- 
pooh  theory.  The  third  is  his  own.  These  original  phonetic 
roots  in  language  are  "phonetic  types  produced  by  a  power  in- 
herent in  human  nature."  "  There  is  a  law  which  runs  through 
nearly  the  whole  of  nature,  that  every  thing  which  is  struck  rings. 
Each  substance  has  its  peculiar  ring."  Man  in  his  primitive  state 
possessed  a  faculty  that  has  now  become  extinct,  since  its  object  is 
fulfilled,  "  by  which  every  impression  from  without  received  its 
vocal  expression  from  within."  By  this  faculty  man  created  these 
phonetic  types  to  an  almost  infinite  extent  at  the  beginning,  but 
by  a  process  of  elimination  reduced  them  ere  long  to  some  four  or 
five  hundred.  This  theory  assumes  this  strange  fact  of  a  primitive 
faculty  now  extinct,  without  a  shadow  of  warrant,  except  the 
necessities  of  the  theory.  It  is,  moreover,  as  unintelligible  as  it  is 
baseless. 

We  must  take  the  fact  that  man  is  capable  of  embodying  his 
cognitions  in  vocal  sounds,  and  is  pressed  by  an  irrepressible  in- 
stinct to  give  such  vocal  expression  to  his  thoughts,  as  an  ultimate 
fact.  Why  he  selects  this  and  not  that  out  of  the  multiplicity  of 
vocal  sounds  to  embody  a  given  thought,  is  a  question  that  can 


230  APPENDIX. 

only  be  answered  generally,  that  the  selection  is  determined  by 
some  accidental  association  at  the  time  of  forming  the  word,  that 
is,  by  some  identification  of  the  thought  with  the  particular  sound 
in  its  nature,  its  condition,  or  relation.  The  object  named  may  be 
a  sound,  and  the  name  may  resemble  that.  It  may  be  one  that 
utters  or  makes  a  sound,  and  the  name  may  be  taken  from  re- 
semblance to  that.  It  may  make  an  impression  that  shall  occa- 
sion an  exclamation,  or  that  shall  be  similar  in  some  respect  to 
that  made  by  another  object  already  named,  and  be  named  accord- 
ingly. It  may  be  associated  with  some  sound  from  other  objects 
at  the  time,  or  it  may  be  associated  with  some  other  words  already 
formed ;  or  still  other  associations  may  exist,  and  so  the  particular 
name  be  determined  as  to  its  sound. 

As  language  may  reasonably  be  supposed  to  have  originated  in 
the  desire  to  communicate,  and  not  in  the  mere  impulse  to  embody 
a  mental  state  in  sound,  we  may  suppose  that  the  first  words  were 
sounds  which  would  be  regarded  by  the  first  speaker  as  associated 
in  some  way  with  the  mental  state  to  be  communicated  as  well  by 
the  person  addressed  as  by  himself.  This  mental  state  may  have 
been  a  sight  of  some  object  visible  to  both,  or  of  some  sound  audi- 
ble to  both,  and  the  sound  adopted  to  express  it  may  have  been 
either  determined  by  some  common  experience  of  a  sound-sensa- 
tion, or  arbitrarily  connected  with  it  by  some  demonstrative  act 
on  the  part  of  the  speaker.  Or  this  mental  state,  to  be  communi- 
cated in  the  primitive  word,  may  have  been  that  of  a  sensation 
through  some  other  sense,  or  through  the  general  sensual  organ- 
ism. What  more  natural  than  to  suppose  that  a  sensation  of  cold 
may  have  prompted  such  primitive  word,  the  sounds  in  which  may 
have  been  such  as  would  naturally  express  shuddering,  as  the  He- 
brew root  Kar  —  cold  ?  What  may  be  thus  supposed  in  regard 
to  the  first  word  actually  spoken  by  man,  may  be  supposed  with 
like  reason  in  regard  to  all  proper  primitives,  or  root-words.  Thus 
we  may  imagine  to  ourselves  how  words  in  the  progress  of  speech 
came  successively  into  being  in  the  instinctive  desire  in  man  to 
communicate  his  own  experiences  to  his  fellow,  which  desire  he 
could  gratify  only  through  sensations  common  to  both  speaker  and 
hearer,  these  sensations  being  identified  by  some  determination  of 
place  or  time,  and  being  as  various  as  the  possible  sensations  of 
which  man  is  susceptible,  that  can  thus  be  identified  by  different 
persons.     It  is  idle  to  argue  in  favor  of  any  one  sense  or  any  one 


APPENDIX.  231 

sensation,  as  furnishing  the  occasion  for  the  production  of  the  prim- 
itive word.  It  is  worse  to  found  a  theory  of  language,  as  some 
able  grammarians  have  done,  upon  the  groundless  assumption  that 
the  primitive  thought,  the  first  experienced  or  communicated,  was 
a  sight  — as  a  motion,  an  activity,  predicated  of  some  object. 


INDEX. 


A. 

Abstraction,  33. 

^Esthetic  whole,  28. 

Affirmative  judgment,  48. 

Amplification  of  concepts,  73. 

Analysis,  33 ;  as  a  process  of  attain- 
ing distinctness,  173. 

Antecedent  of  a  reasoning,  93. 

Apodictic  judgment,  51. 

Argumentation,  92. 

Assertory  judgment,  51. 

Attention,  34. 

Attributes,  their  various  denomina- 
tions, 19,  20. 

Axioms,  61. 

B. 

Base  of  a  concept,  63. 

Begging  the  question,  fallacy  of,  191. 


c. 

Categorical  judgment,  53. 

Categorical  syllogism,  103  ;  two 
kinds,  deductive  and  inductive, 
105;  its  subjective  law,  190. 

Causal  analvsis,  174;  how  perform- 
ed, 179 ;  its  law,  179. 

Causal  judgment,  58;  rules  of,  155. 

Causal  whole,  27,  28. 

Chain  of  reasoning,  128. 

Characters,  a  designation  of  attri- 
butes, 20. 

Circle,  fallacy  of,  192. 

Classification,  80. 

Clearness  a  virtue  in  the  formal  per- 
fection of  science,  136 ;  attained  by 
definition,  104. 


Coextension  in  concepts,  78. 

Collective  whole,  27. 

Comparison,  34. 

Completeness,  law  of,  174. 

Composition,  a  variety  of  immediate 
reasonings,  102. 

Composition  and  Division,  fallacy  of, 
191. 

Comprehensive  judgment,  56;  rules 
of,  155. 

Comprehensive  quantity  of  a  con- 
cept, 73. 

Comprehensive  whole,  28. 

Concept,  formation,  62  ;  definition, 
63  ;  under  law  of  Identity,  63  ;  a 
relative  and  one-sided  cognition, 
64;  not  a  reality,  65;  how  to  be 
realized,  66;  a  quantity,  72;  am- 
plification, 73;  relations  of  in  ex- 
clusion, coextension,  subordina- 
tion, coordination,  intersection, 
78  ;  identical  and  different,  86  ; 
opposition,  congruent  and  confiict- 
ive,  87;  intrinsic  and  extrinsic, 
89  ;  methodology,  157  ;  threefold 
perfection,  157 ;  objective  law,  157; 
correspondence  with  realities,  160- 
162;  subjective  law,  163;  verbal 
law,  181. 

Concept  words,  their  genesis,  139- 
144. 

Concretion,  75. 

Conditional  syllogism,  118  ;  two 
modes,  ponent  and  tollent,  119; 
distinguished  in  respect  to  quan- 
tity into  hypothetical  and  disjunct- 
ive, 120. 

Congruence,  a  virtue  in  the  formal 
perfection  of  science,  138. 

Consequent,  a  part  of  a  reasoning, 
93. 


234 


INDEX. 


Consequents,  a  designation  of  attri- 
butes, 20. 

Conspecies,  85. 

Contradiction,  law  of,  24. 

Conversion,  96;  its  subjective  law, 
187. 

Coordination  of  notions  extensive, 
78;  intensive,  89. 

Copula  of  a  judgment,  38. 

Corporate  whole,  29. 

Correctness,  a  virtue  in  the  verbal 
perfection  of  science,  144. 

Correspondence  between  thought 
and  reality,  162. 

D. 

Deductive  syllogism,  105 ;  two  kinds, 
extensive  and  comprehensive,  109 ; 
its  subjective  law,  190. 

Definition,  the  process  for  attaining 
clearness,  164:  import  of,  161;  its 
kinds,  168 ;  verbal,  real,  and  genet- 
ic, 169. 

Definitives,  141. 

Demonstrable  propositions,  60. 

Determination  of  concepts,  74. 

Determinations,  a  designation  of  at- 
tributes, 20. 

Dianoetic  whole,  27. 

Differences,  a  designation  of  attri- 
butes, 20. 

Dilemma,  a  kind  of  judgment,  55; 
a  kind  of  syllogism,  122 ;  its  sub- 
jective law,  204. 

Discourse,  92. 

Discrete,  or  disjunct  notions,  85. 

Disjunction,  law  of,  24;  a  variety 
of  immediate  reasonings,  102. 

Disjunctive  judgment,  48;  its  three 
forms,  48 ;  rules  of,  149,  150. 

Disjunctive  syllogism,  125;  ponent 
and  tollent  modes,  126;  its  subject- 
ive law,  203. 

Dissection,  a  process  of  logical  anal- 
ysis, 173  ;  its  two  kinds,  special 
and  numerical,  175. 

Distinctness,  a  virtue  in  the  verbal 
perfection  of  science,  138;  attained 
by  analysis,  164  ;  its  conditions, 
173 ;  its  law,  173. 

Division,  a  process  of  logical  analysis, 
174;  how  performed,  176;  its  law, 
177,  178. 

E. 

Elements  of  thought,  laws  and  prod- 
ucts, 17. 


Enthymeme,  94. 

Epichirema,  129. 

Epithets,  141. 

Essential  whole,  27. 

Evolution,  or  causal  analysis,  174  ; 
how  performed,  179 ;  its  law,  179. 

Exclusion,  law  of,  25 ;  relation  of  in 
concepts,  78. 

Exercises  in  judgments,  207;  in  con- 
cepts, 214 ;  in  reasonings,  214. 

Experimental  propositions,  61. 

Extensive  deductive  syllogism,  109- 
111. 

Extensive  judgment,  56  ;  rules  of, 
155. 

Extensive  quantity  of  a  concept,  73. 

Extensive  whole,  28. 

F. 

Fallacies  to  be  detected,  217. 

Fallacy  of  composition  and  division, 
191  ;  of  unreal  universality,  191 ; 
petitio  principii,  191 ;  hysteron  pro- 
teron,  192 ;  of  the  circle,  192 ;  saltus, 
192;  ignava  ratio,  193;  non  causa 
pro  causa,  or  post  hoc  ergo  propter 
hoc,  195. 

Formal  perfection  of  science,  137; 
its  three  virtues  —  clearness,  con- 
gruence, distinctness,  138. 

Formal  whole,  29. 

G. 

Generalization,  74,  80. 
Generic  difference,  84. 
Genus,  82 ;  of  two  degrees,  83. 
Geometrical  whole,  27. 


H. 

Heterogeneity,  law  of,  86. 
Hindoo  system  of  reasoning,  107. 
Homogeneity,  law  of,  86. 
Hypothesis,  61. 
Hypothetical  judgment,  54;  rules  of, 

153. 
Hypothetical    syllogism,    120;    two 

modes,  ponent  and  tollent,  120 ;  two 

varieties  —  proper  hypothetical  and 

dilemma,  122;  its  subjective  law, 

202. 
Hypothetico  -  disj  unctive  j  udgment, 

55. 
Hypothetico  -  disjunctive   syllogism, 

122;  subjective  law,  204. 
Hysteron  proteron,  fallacy  of,  192. 


INDEX. 


235 


I. 

Identical  judgment,  53. 

Identical  notions,  86. 

Identity,  law  of,  24. 

Iqnava  ratio,  fallacy  of,  193. 

Illation,  92. 

Immediate  reasoning,  93,  94. 

Indemonstrable  propositions,  60. 

Individual  difference,  84. 

Induction,  its  nature,  223. 

Inductive  syllogism,  112-118;  its 
subjective  law,  195. 

Inference,  92. 

Integrate  judgment,  57";  rules  of, 
155. 

Integrate  whole,  27. 

Intensive  deductive  syllogism,  109- 
111. 

Intensive  judgment,  56 ;  rules  of,  155. 

Intensive  quantity  of  a  concept,  73. 

Intensive  whole,  28. 

Investigation  and  probation  distin- 
guished, 183. 

Involution  of  concepts,  89. 


J. 

Judgment  denned,  31;  parts,  35; 
division,  39-47;  judgments  in  re- 
lation to  one  another,  58 ;  method- 
ology, 147  ;  three  conditions  of 
perfection  in  judgments,  material, 
formal,  and  verbal.  147;  rules  of  a 
perfect  judgment,  148, 155, 156. 


L. 

Language,  its  relation  to  thought, 
69,  138-144;  its  origin,  227. 

Laws  of  thought,  four  in  number,  21; 
how  evolved,  21-24;  of  identity, 
24  ;  of  contradiction,  24  ;  of  dis- 
junction, 24  ;  of  exclusion,  25  ; 
subjective  and  objective  laws,  25. 

Lemmata,  61. 

Logic  defined,  1 ;  whether  an  art  or 
a  science,  1  ;  its  object  matter, 
thought,  2;  its  objective  utility  as 
science  of  thought,  3  ;  as  pure 
science,  4;  its  subjective  utility  as 
aid  to  discovery,  6 ;  as  builder  of 
science,  6  ;  as  corrective  of  error, 
9;  as  assuring  truth,  9;  as  invig- 


orating the  understanding,  10 ;  as 
affording  a  nomenclature,  10  ;  its 
divisions,  objective  and  subjective, 
12 ;  abstract  and  concrete,  12 ;  pure 
and  modified,  15  ;  parts  of  pure 
logic  —  doctrine  of  elements  and 
doctrine  of  method,  16. 

Logical  definition,  169. 

Logical  quadruped,  fallacy  of,  190, 
191. 

Logical  whole,  its  two  species,  ex- 
tensive and  intensive  or  compre- 
hensive, 28. 


M. 

Major  premise,  107. 

Major  term  in  a  syllogism,  106. 

Marks,  a  designation  of  attributes, 
20. 

Mass  whole,  27. 

Material  perfection  of  science,  136  ; 
its  two  virtues,  adequateness  and 
accuracy,  137. 

Mathematical  whole  —  numerical 
and  spacial,  27. 

Mediate  reasoning,  94;  of  two  class- 
es, 102. 

Method  what,  132 ;  its  different  ends, 
132. 

Methodology,  132;  its  divisions,  145; 
of  judgments,  147  ;  of  concepts, 
157 ;  of  reasonings,  183. 

Middle  term  in  a  syllogism,  106. 

Minor  premise,  107. 

Minor  term  in  a  syllogism,  106. 

Modal  judgments,  rules  of,  51. 

Modal  restriction,  a  variety  of  imme- 
diate reasonings,  98;  its  subjective 
law,  188. 

Modality  of  a  judgment,  40. 

Modes  of  cogitable  matter  denoted 
by  various  terms,  19. 

Monosyllogism,  128. 


N. 

Necessary  judgment,  51. 

Negative   judgment,   48  ;    rules  of, 

149. 
Non  causa  pro  causa,  fallacy  of,  195. 
Notes,   a   designation   of  attributes, 

20. 
Numerical  difference,  84. 
Numerical  whole,  27. 


236 


INDEX. 


o. 

Objective  law  of  a  judgment,  148; 
of  a  concept,  157 ;  of  a  reasoning, 
184. 

Opposition  in  logic,  48  ;  contradic- 
tory, 49,  88;  contrary,  49,  88. 


P. 

Partial    judgment,    53;     rules    of, 

152. 
Particular  notions,  80. 
Partition,  a  process  of  logical  anal- 
ysis, 174 ;  how  performed,  178 ;  its 

law,  178, 179. 
Perspicuousness,    a   virtue    in    the 

verbal  perfection  of  science,  144; 

its  subordinate  qualities,  145. 
Petilio  principii,  fallacy  of,  191. 
Polylemma,  123. 
Polysyllogism,  94,  128  ;  two  kinds, 

Epichirema     and    Sorites,     129; 

mode  of  verifying,  205. 
Ponent    mode    of    the    conditional 

syllogism,  119. 
Post  hoc  ergo  propter  hoc,  fallacy  of, 

195. 
Postulate  of  logic,  29. 
Postulates,  61. 
Practical  propositions,  60. 
Praxis,  207. 
Predicables,  predicates,  predicaments, 

designations  of  attributes,  or  modes 

of  being,  20. 
Predicate  of  a  proposition,  35. 
Principle  of  division,  176. 
Probation  and  investigation  distin- 
guished, 183. 
Problematic  judgment,  51. 
Problems,  60. 
Products  of  thought,  31. 
Progressive  syllogism,  129. 
Properties,  designations  of  attributes, 

20. 
Proposition,  31. 
Pure  logic,  its  divisions,  16. 


Qualities,  their  various  denomina- 
tions, 19. 

Quantitative  restriction,  97 ;  its  sub- 
jective law,  188. 

Quantity,  relation  of,  in  all  thought, 
25;    of    concepts,  extensive    and 


intensive,    72 ;    these    quantities 
how  opposed  to  each  other,  77. 


R. 

Ratiocination,  92. 

Eeasoning,  defined,  91;  how  denom- 
inated, 92;  its  parts,  93;  immedi- 
ate reasonings,  93;  mediate,  94; 
methodology  of  reasonings,  183; 
objective  law,  184;  subjective  law, 
185  ;  complex  reasonings  to  be 
resolved  for  separate  verification 
of  parts,  185-187. 

Regressive  syllogism,  129. 

Representative  whole,  29. 

Resolution,  a  process  of  logical  anal- 
ysis, 194  ;  how  performed,  179  ; 
its  law,  179. 


s. 

Sallus,  fallacy  of,  192. 

Scholia,  61. 

Science,  its    threefold  perfection  — 

material,  formal,  and  verbal,  133. 
Sentence,  31. 
Signs,   a   designation  of  attributes, 

20. 
Sorites,  94,  130. 
Spacial  whole,  27. 
Species,  80;  of  two  degrees,  83. 
Specific  difference,  84. 
Specification,  80,  82. 
Subject  of  a  proposition,  35. 
Subjective  law  of  a  judgment,  148; 

of  a  concept,  164 ;  of  a  reasoning, 

185. 
Subordination  of  notions,  78,  79. 
Substantial  judgment,  57  ;  rules  of, 

155. 
Substantial  whole,  27. 
Subsumption,  108. 
Sumption,  107. 

Syllogism,  92,  93;   single,  94;  poly- 
syllogism,   94  ;    categorical    and 

conditional,  94. 
Synthesis,  34. 


T. 

Tautological  judgment,  53. 

Terms  of  a  judgment,  35-38;  three 

gradations,  37  ;    in  a  syllogism, 

106. 


INDEX. 


23T 


Theorems,  61. 

Theoretical  propositions,  60. 

Thought,  the  object  matter  of  logic, 
2;  its  narrower  import  as  product 
of  the  discursive  faculty,  2;  its 
essential  nature,  17  ;  a  relative 
cognition,  or  a  cognition  of  a  du- 
ality of  cognitions,  17;  its  four 
fundamental  laws,  21 ;  its  products, 
31;  its  relations  to  its  matter, 
136. 

Tollent  mode  of  the  conditional  syl- 
logism, 119. 

Topics  for  discussion  or  investiga- 
tion, 221. 

Transference,  a  variety  of  immediate 
reasoning,  98  ;  its  two  kinds,  as 
qualitative  and  modal,  101 ;  its 
law,  189. 

Trilemma,  123. 


u. 

Universal  notions,  80. 

Unreal  universality,  fallacy  of,  191. 

Utility  of  logic,  2. 


V. 

Verbal  law  of  a  judgment,  148;  of  a 

concept,  181. 
"Verbal  perfection  of  science,  138 ;  its 

two  virtues,  correctness  and  per- 

spicuousness,  144. 


w. 

Wholes  in  thought  enumerated,  27; 
per  se,  27 ;  per  accidens.  29. 


THE  EHD. 


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